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Chapman, Randall G.; Jackson, RexCollege Choices of Academically Able Students: TheInfluence of No-Need Financial Aid and Other Factors.Research Monograph No. 10.College Entrance Examination Board, New York, N.Y.ISBN-0-87447-279287123p.College Board Publications, Box 886, New York, NY10101 ($12.95).Reports - Research/Technical (143)Tests/Evaluation Instruments (160)

MF01 Plus Postage. PC Not Available from EDRS.Academic Ability; *Academically Gifted; *CollegeApplicants; *College Choice; Decision Making;Enrollment Influences; Higher Education; HighSchools; High School Students; *Merit Scholarships;Models; *No Need Scholarships; Questionnaires;Student Attitudes; *Student Financial Aid

ABSTRACTCollege preferences and choices of a sample of

high-ability high school seniors applying to colleges in spring 1984were studied to determine the award of no-need (merit) aid to thestudents and the degree to which such aid influences college choices,in relation to other factors. A multistage model of college choicebehavior was employed that focuses on perception formation,preference judgment formation, and choice. The study is based on anational probability sample of 2,000 high-ability high school seniorswho had taken the College Board's Scholastic Aptitude Test (SAT).Students were contacted before and after the actual college choicedecision. A total of 1,183 students who had applied to at least twocolleges were surveyed by mail and interviewed. Sixty-four percent ofthese students, received at least one offer of financial aid. Resultsindicate that most colleges consider a student's academic ability indetermining whether a student receives financial aid and the size ofthe aid package. Monetary factors were important to college choice;however, the primary determinant of college choice was perceivedcollege quality. Appendices include information on the multinomiallogit model, the mail questionnaire, and the interview schedule.(SW)

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College Choices of AcademicallyAble Students:The Influence ofNo-Need Financial Aid and Other FactorsRandall G. Chapman and Rex Jackson

'PERMISSION TO REPRODUCE THISMATERIAL IN MICROFICHE ONLYHAS BEEN GRANTED BY

U.S. DEPARTMENT OF EDUCATIONCOce d Educetional Research arid Movement

EDUCATIONAL RESOURCES INFORMATIONCENTER (ERIC)

taredocument hea been mproduced asreceived from the WWI or organizationoriginating it.

O Minor changes have been made to improverepeoduchtm quaMT

College Choicesof Academically Able Students

The Influence of No-Need Financial Aidand Other Fators

Research Monograph No. 10

by Randall G. Chapman

University of Alberta

Rex Jackson

Applied Educational Research, Inc.

College Entrance Examination Board, New York, 1987

Authors are encouraged to express freely theirprofessional judgment. Therefore, points of view oropinions stated in College Board books do notnecessarily represent official College Board positionor policy.

Inquiries regarding this publication shouldbe addressed to Editorial Office, The College Board,45 Columbus Avenue,New York, New York 10023-6917.

Copies of this publication may be ordered fromCollege Board Publications, Box 886,New York, New York 10101. The price is $12.95.

Cover photograph by Glenn Foss.

Copyright © 1987 by College Entrance Examination Board.All rights reserved. The College Board. Scholastic AptitudeTest, SAT, College Scholarship Service, css, and the acornkRo are registered trademarks of the College Entrance Ex-am'nation Board.

Library of Congress Catalog Card Number: 86-073023

ISBN: 0-87447-2792

Printed in the United States of America.

9 8 7 6 5 4 3 2 1

4

Contents

Acknowledgments1. Introduction and summ3ry of principal

findings 1

2. A comprehensive model Of collegechoice behavior: Theory andmeasurement 11

3. Study design and data ;:ollection 234. Determinants of college choice

behavior 275. Determinants of financ:al aid awar& . . 556. Antecedents of college choice

behavior: Preference judgmentformation 66

7. Antecedents of college choicebehavior: Perception judgmentformation 77

8. Other factors influencing collegechoice behavior: Campus visits andpost-admissions contacts 86

9. Changes in college choice after theinitial decision 91

Appendixes1. An over/iew of the multinomial

logit model 952. The mail questionnaire 993. The telephone interview instrument. . . 1044. ko illustrative choice probability

calculation 113References 115

5

Acknowledgments

The authors gratefully acknowledge the financialsupport and sponsorship of the College Board.

Preliminary reports of this study's findingswere presented at the National Forum of the Col-lege Board (New York, October 1984) and at theMiddle States Regional Meeting of the CollegeBoard (Washington, February 1985). Study find-ings were also presented at two day-long work-shops held in connection with the New Englandand Midwest Regional Meetings of the CollegeBoard. These "Financial Aid and EnrollmentMarketing" workshops were held in Newton,Massachusetts and in Chicago in February 1986.The comments of the participants at these meet-ings and workshops were helpful in shaping thefinal study report and in suggesting a number ofuseful additional analyses.

The authors wish to express their particularappreciation to James Nelson of the CollegeBoard for his early participation in study planningand his continuing encouragement throughout theproject. They also wish to acknowledge the con-tribution of D. F,Iwin Lebby and Caroline Cuth-bert of Annap: search and CommunicationsAssociates in ci ..ting the telephone interview-ing for with this project. Shannon Gangl providedhelpful research and computing assistance in theearly stages of the data-analysis phase.

The authors assume full responsibility for thecontents of this report and for any remaining er-rors. The authors are listed in alphabetical order.

6

1. Introduction and summaryof principal findings

This chapter describes the purpose of the studyand the organization of the report, and it providesa description of the r?search design and a sum-mary of the main study findings.

Our conclusions are based on a large-scale sur-vey research study, sponsored by the CollegeBoard, concerned with the college preferencesand choices of a sample of high-ability high schoolseniors applying to colleges in the spring of 1984.The main objective of this research effort was toassess the degree to which high school studentswith high academic ability are currently beingawarded aid on a no-need (or "merit-) basis andthe degree to which such financial aid influencescollege choices, in relation to other factors.

Study background and contextSeveral concerns prompted the initiation of thisstudy. Surveys of institutions concerning their fi-nancial aid policies suggest that the number ofcolleges awarding some aid on a no-need or aca-demic basis, without regard to financial nee,-:' con-siderations, is growing. Several surveys in themid-to-late 1970s (Huff 1975: Sidar and Potter1978: the College Board/AACRAO 1980) providedestimates that about 55 to 65 percent of four-yearcolleges and universities used no-need criteria in

making financial aid awards. More recently, in asurvey conducted by tbe College Board and theNational Association of Student F;nancial AidAdministrators (NASFAA) in 1984, 85 percent offour-year private colleges responding to the sur-vey and 90 percent of four-year public collegesstated that they offered some awards on an aca-demic basis without regard to financial need con-siderations.

For colleges responding to the 1984 CollegeBoard/NASFAA survey, the average no-needaward was $835 for public institutions (with 80percent of the awards under $1,000) and $1.558for private institutions (with 51 percent und..-r$1,000). However, some awards are appreciablylarger than these figures suggest. For example,private colleges reported that 20 percent of cheirno-need aid awards exceeded $2,000, and 6 per-cent exceeded $4,000.

Many colleges have always had some scholar-ships for which financial need has not been arelevant consideration in the awarding decision.However, the use of financial aid as an enrollmentinducement has apparently become increasinglywidespread in recent years. In the College Board/NASFAA survey, about 36 percent of the publicand 51 percent of the private colleges stated thatno-need awards were used primarily as a recruit-ment device, in contrast to a means for recogniz-ing outstanding achievement. In another recentsurvey (Porter and McColloch 1982), 80 percentof colleges awarding no-need aid reported that

such aid was used eithel to "a great extent- orto "some extent- in recruiting. It seems clear.therefore, that attracting academically able stu-dents to the campus is at least one of the motivesunderlying many institutions' use of no-need fi-nancial aid awards.

Study focus and approachFrom a research pe-spective. the relevant issuesbecome those of determining the real impact ofno-need awards on the college choices of thehigh-ability students who are the target of suchscholarships. Presuming that these awards do in-fluence students' college choices in a materialfashion, some policy analysis inquiries naturallyfollow. Of particular concern would be how col-leges might compete for high-ability students inother ways than just resorting to no-need schol-arships of their own. This involves identifying andquantifying the role of other, nonmonetary factorsin the college choice decision-making process.Cost-benefit analyses are relevant here, too.What is the cost of using no-need scholarships?Are there other more cost-effective ways to at-tract high-ability students?

Since the focus of this study is on no-needfinancial aid awarded on the basis of academiccriteria, the relevant study population is high-ability high school students. These are the stu-dents who will attract the no-need awards, sincethe purpose of such awards increasingly appearsto be to encourage particularly desirable studentsto enroll at a college. Here. "desirable- is pre-sumed to be defined in the usual academic terms.To many colleges, it may include other consid-erations as well, including those of athletic abilityor leadership skills and potential. This study isprincipally concerned. however, with the influ-ence of financial aid on college choice and withthe use of academic criteria by colleges in makingaid awards.

8

Organization of the reportThis report is organized into three main partsdescribing our approach to the research problem.our findings on the main research questions re-lated to the determinants of college choice be-havior of high-ability students. and findings onauxiliary issues associated with the college choiceprocess.

The first part of this report provides a descrip-tion of the theoretical fram 'work for this researchand a discussion of a number of methodologicaland measurement issues associated with studyingcollege choice behavior (Chapter 2).

The second part describes the study of collegechoice and financial . 1 awarding behavior, in-cluding: a descriptim f the study design andassociated data collection procedures (Chapter3); presentation and discussion of empirical find-ings with respect to the role of college costs andfinancial aid in relation to other factors in deter-mining high-ability students' college choices(Chapter 4); and presentation and discussion ofempirical findings with respect to determinantsof colleges financial aid awards (Chapter 5).

The final section provides descriptions of em-pirical findings on other aspects of college choicebehav'r, including: antecedents of choice behav-ior, including preference judgment formation(Chapter 6) and perception judgment formation(Chapter 7); other influences on choice behavior,including college campus visits and post-admis-sions contacts (Chapter 8); and changes in collegeplans after initial decisionsactual fall enroll-ment compared to choices reported in the spring(Chapter 9).

The theoretical frameworkTo assess the role of no-need awards on the col-lege choices of high-abi'ity high school students,

2

we have constructed a general model of collegechoice behavior. The fundamental premise un-derlying this reseP rch effort is that the role offinancial aid in c,c.ieraland no-need awards inparticularas a determining factor in collegechoice may be assessed only within the contextof all the other factors at work when studentscholse colleges. It is impossible to assess the roleofiv single factor in a complex decis;on processlike college choice except relative to other con-siderations.

The major support for this premise comes frompast studies of the college choice process, suchas those of Radner and Miller (1975), Kohn, Man-ski, and Mundel (1976), Chapman (1979), andManski and Wise (1983). These studies demon-strate that college quality, reputation, and pres-tige appear to be the most important considera-tions in the college choice process. Financialconsiderations certainly exist, but they seem tobe of secondary importance. Nonetheless, thekey question is still how important the monetaryconsiderations are relative to other factors. Thecarrent study was designed specifically to gatherthe most extensive data to date on financial aidin general, and no-need financial aid awards inparticular, in order to address this issue of therelative importance of financial aid.

Our multistage model of college choice behav-ior consists of three major components: percep-tion formation, preference judgment formation.and choice. We seek to explain the determinantsof how students perceive colleges (what objec-tively verifiable college attributes are related tostudents' perceptions), how these perceptions areimplicitly combined and weighed to form an over-all summary measure of the "value" of a partic-ular college to a student (prior preference). ani:'ultimately how prior preference and other factors(such as monetary considerations) lead to actualobserved college choices. Because of our partic-ular concern with the influence of financial aid

on students' college choices, we have studied andanalyzed the final phases (preference and choice)in the greatest detail. Chapter 2 describes themultistage model of college choice behavior usedthroughout this study as a framework for studydesign, data organization, and analysis.

Study design and data collectionMost studies of college choice, guch as insLitu-tional "yield rate" studies, collect data for sam-ples of students who have all been admitted to agiven institution. In such admitted applicantstudies, information is gathered only after finalchoices are made. In contrast, this study is basedon a national probability sample of 2,000 high-ability high school seniors who had taken theCollege Board's Scholastic Aptitude Test (SAT).Students in the sample were contacted twice,before and after the actual college choice deci-sion.

The sample of students was first surveyed inMarch 1984 by means of a mail questionnaire.Information was sought with regard to the coi-leges to which students had applied, their currentrankings of the top three colleges in order ofpreference, self-reported importance weights fr rfactors in college choice, and their ratings of thetop three colleges based on these factors.

Those students who had responded to the firstsurvey and who had reported applying to morethan one college were contacted again by tele-phone in MayJune 1984. Trformation gatheredduring this --cond phase inc*.uded the status ofadmissions offers received, specific financial aidoffers made by those colleges offering admission,and the final choice of college to attend.

Thus, within this multistage study design, weare able to analyze the preferences stated by stu-dents et a time before aid offers from most col-leges were known, the actual aid offers later re-ceived, and final choices. As a consequence, we

3

are able to isolate the effects of aid offers and toassess their influence on choices after taking intoaccount prior preferences.

A total of 1,549 relponses to the mail surveywere obtained, representing a response rate of77.5 percent. Of these respondents, 325 reportedthat they had applied tc (and in virtually all casesbeen accepted by) a single college. Of the re-maining 1,224 students who had applied to atleast two colleges, 1,183 were eventually con-tacted by telephone, for a response rate to thetelephone survey of 96.7 percent.

Chapter 3 describes the study-design and data-collection methodology in detail.

Determinants of choice behaviorChapter 4 contains a complete description of thestudy findings with regard to the determinants ofcollege choice behavior. Here, a brief overview isprovided.

Preliminary remarksGiven our two-stage research design, it was pos-sible to separate a student's prior preference fora college from his actual choice behavior. Priorpreference is unconstrained by whether the stu-dent was admitted to a college but alsomostimportantit is designed to be independent ofmonetary considerations. Monetary considera-tions. and other situational constraints, are fac-tored back in the choice equation in the actualchoice phase.

It is important to note that we are studyingcollege choice behavior, not college search be-havior. Our study begins at the point where stu-dents have formed their application sets, the col-leges to which they have submitted applications.We must presume that all such colleges are min-imally satisfactory on all major dimensions ofchoice or else would have been excluded from theapplication set. However, since students do notknow their exact out-of-pocket costs until theyreceive financial aid offers. costs may act also as

a constra;nt on final choices, making the selectionof some college options infeasible.

Major resultsAbout 61 percent of our students with choice setsof two or more actually chose to attend their orig-inal highest-preference college (to which theywere admitted). The remaining 39 percentswitched from their original highest-preferencecollege to another college. We need to examinethe forces which led some students te followthrough with their original preferences whileothers switched. Those who switched mentionedthe following major factors as being influential:better financial aid (27.4 percent). lower costs(23.1 percent), campus visits (12.6 percent), lo-cation (11.9 percent). and academic reputatiG.(11.9 percent). Thus, over half these students re-ported money as a factor in their switching. (Ininterpreting these findings, it is important to notethat direct self-reports for those students whoremained loyal to their original first-choice col-lege were not collected, so comparisons betweenthose who switched and those who remained loyalis not possible.)

While these self-reported reasons for changesin choice are of general interest, it is importantto note that such self-reports are subject to avariety of possible distortions. In general, infer-ences drawn from actual choice behavior and theobjective correlates of that behavior are morelikely to be dependable. For this reason, the mainfocus of our analysis is on the development andestimation of a statistical model of college choicebehavior. This model provides estimates of therelative importance of a number of factors in in-fluencing college choices. Most important, thestatistical model usedthe multinomial logitmodelprovides quantitative estimates of collegechoice determinants. thus making it possible toassess, for example, how much choice rrobabil-ities change in response to changes in financialaid.

1 04

Our results indicate that prior preference for acollege is the primary and paramount determi-nant of college choice behavior. Operationally,prior preference was assessed by means of therankings of the top three colleges provided bystudents in the first-stage survey. These earlierpreferences dominate all other factors in thechoice of a college. Other statistically meaningfuldeterminants of college choice do exist, but priorpreference is the predominant indicator of whichcollege a student will ultimately choose.

Monetary considerations have a smaller butstatistically detectable influence on collegechoice. Other things being equal, total collegecosts detract from a college's attractiveness,while scholarship aid adds to its desirability.Other non-grant components of financial aid.such as loans and part-time jobs, appear to haveno influence on college choice behavior.

The relatively modest role played by monetaryconsideraLions might well have been expected inthe context of a study of college choice. Collegeswhich were perceived to be too expensive (eventaking into account expected financial aid) mayhave been ruled out of consideration during thecollege search phrase. prior to the formation ofan application set. Also, this finding is in accordwith the empirical results of previous studies ofcollege choice behavior: college quality is the pri-mary determinant of college choice, with financialconsiderations being of secondary importance.

Another factor influencing college choice be-havior is the student's perceived chance of havinga financial aid offer renewed: greater perceivedrenewability is positively related to choice. Stu-dents seem to implicitly discount scholarship aidthat is only offered on a one-time basis. with littleor no chance of beibg renewed. The magnitudeof this implicit discounting is substantialsomuch so that colleges should probably not evenoffer such nonrenewable aid.

Students appear to prefer colleges whose aca-demic level (as measured by SAT scores) is com-

parable to their own. Thus, an "academic qualityzoning" hypothesis is supported by our results:students prefer colleges that eruoll students withacademic abilities like their own.

A number of other potential influencers andmoderators of choice behavior were examined: (a)whether a student's father or mother attended acollege; (b) the distance from a college's campusto a student's residence; (c) portable financial aidfrom state and private scholarship programs; and(d) whether a student had applied for financial aidbut had not been offered it a college. None ofthese factors had any statisacally significant in-fluence on college choice behavior, given thepresenc of the other variables (described above)in the model. Of course, certain of these variablesmay have been influential when students formedtheir application sets. However, after the appli-cation set formation decision, these variables ap-pear to have no material influence on the ultimatecollege choice behavior of high-ability high schoolseniors.

Implications of the resultsThe statistical modeling approach employed inthis study yields estimated relative importanceweights which measure the implicit trade-offshigh-ability students make when they chooseamong various colleges to which they have beenadmitted. Thus, for example, it is possible toestimate the amount of scholarship aid that wouldapproximately offset a college being a second-choice rather than a first-choice alternative, on aprior preference basis. It is also possible to esti-mate the implicit discounting that high-abilitystudents attach to aid which is perceived to benonrenewable. In addition, it is possible to con-struct elaborate and realistic choice scenar;osand to use the relative importance weights incombination with the statistical model of choice(the multinomial logit model) to predict the like-lihood of students choosing certain colleges underspecified choice situations.

Chapter 4 describes the detailed empirical find-ings with regard to the determinants of collegechoice behavior. A number of sample scenariosand trade-off situations, similar to those de-scribed below, are used to illustrate this study'sfindings regarding the factors at work when high-ability students make college choice decisions.Additional cost-benefit analyses regarding the useof scholarship aid are examined in Chapter 4.

The influence of scholarship aid on choice. Theinfluence of scholarships on college choice be-havior can be illustrated by considering a studentwho is "indifferent" between two college alter-natives. That is, considering all factorsinclud-ing prior preference, college costs, financial aid.perceived renewability of the aid, and the aca-demic "fit" of the student at the colleges (in termsof SAT scores)our hypothetical high-ability stu-dent equally prefers two colleges. The probabilityof such a student choosing each college wauld be50 percent. Alternatively, 100 such students who.on average, are indifferent between two collegealternatives would be expected to ultimately splittheir choices 50-50 between the two colleges.

Now, suppose that one of the colleges offers anadditional amount of scholarship aid, either in theform of a no-need aid award or by enriching theexisting financial aid package to have a greatercomponent of grant (as compared to loans andpart-time jobs). Our statistical model shows pre-dictions (Table 1.1) of the student's revisedchoice probabilities, depending on the amount ofaid offered.

Table 1.1 suggests that scholarship aid will influ-ence high-ability students to some extent. How-ever, substantial amounts of aid are required toaffect choice materially. It should be noted thatthis illustration applies only to a specific hypo-thetical situation: that of a student who is facinga choice between two colleges and is not predis-posed toward either (both colleges are equallypreferred). Different assumptions about thechoice situation will, of course, lead to different

Table 1.1. Illustrative probabilities andeffective costs

Amount ofextragrant

Revised probabilityof choosing the collegeoffering the extra grant (%)

Effectivescholarshipcostper student

$ 0 50.0 $ 0$1,000 57.2 $ 7,944$2,000 64.1 $ 9,092$3,000 70.5 $10,317$4,000 76.2 $11,634$5,000 81.1 $13,039

results. Several more complex and realistic situ-ations are illustrated below and in Chapter 4.

Note that in Table 1.1 the effective scholarshipcost per additional stL lent per year to the collegeis considerably above the actual scholarshipvalue. This occurs because some of the studentswith 50-50 choice probabilities would have en-rolled without such scholarships. (This situation,and the definition and calculation of effectivecosts, is discussed further in Chapter 4.)

Scholarship aid, prior preference, and choice.Another way to illustrate the impact of scholar-ships on college choice behaNior is by consideringhow much extra scholIrship aid would be re-quired to offset the disadvantage of not being theoriginal first-choice prior preference college.Consider a hypothetical student with two collegesin his or her choice set which are similar on allfactors except for original first-choice prior pref-erence. In such a case, our results imply that, onaverage, the original first-preference collegewould be chosen by the student about 80 percentof the time. Our results predict that the originalsecond-choice college would have to offer an ad-ditional scholarship of about $4.700 to improveits chances of choice to 50 percent (from 20 per-cent).

This result illustrates the primacy of prior pref-erence over money: prior preference is extremelyimportant to high-ability students, and monetary

12

considerations are secondary in influence. In ef-fect, high-ability students tend to choose the col-lege that they view most highly, almost regardlessof the financial consequences. However, a rela-tively large amount of scholarship aid has, asmight be expected, some influence on the collegechoices of these students.

An illustration of choice between private andpublic colleges. A typical scenario involving theuse of no-need aid is for a high-cost private col-lege t^ offer such financial support to competemore la. arably with a low-cost public institution.Of course, other considerations (such as per-ceived relative college quality) may operate infavor of the private college. Our results shed lighton the costs associated with .,uch no-need aidaward actions on the part ol the (relatively) high-cost private college. The use of no-need schol-arship aid will improve the likelihood of the stu-dent choosing the no-need, aid-awarding coll 4e.However, the key issue concerns how sensitivethe choice probabilities are to no-need aid andalso, from the college's perspective, the expectedcost of pursuing such a policy.

To investigate the economics of awarding suchno-need aid, we will assume that the student inquestion is from a high-income family (in whichcase no-need aid is the only kind of financial aidthat could be offered). This high-income assump-tion is important. As discussed in Chapter 4,there are some differences in the implicit relative-importance weights used by students in variousincome strata. See Chapter 4 for details on thesedifferences.

The following additional assumptions are madein this scenario:

College A College B(private) (public)

Total costsGrant aid offeredRenewal of grantaid?SATFIT

$12,000 $5,000To be determined NoneIs guaranteed Not relevant

100 150

SATFIT is the difference (in absolute value) be-tween the student's SAT score and the averageSAT scores of all students at a college. All otherconsiderations not mentioned above are assumedto be equal for both colleges (except when mod-ified in the following discussion and analysis).

In this situation, our statistical model predictsthat the base choice probability when college Aoffers $0 of no-need aid is 42.8 percent (assumingthat colleges A and B are equally preferred on aprior-preference basis). The substantial disad-vantage that college A faces with much highercosts is only partially offset by a better SATFIT(100 versus 150).

Some alternative situations involving variousamounts of no-need scholarship aid (from $0 to$5,000) and various prior preference situationsare displayed in Table 1.2.

The last case described in Table .2when theno-need aid awarding college is not the originalfirst-choice prior preference collegeis particu-larly noteworthy. The private college that usesno-need aid to compete with an otherwise pre-ferred (on a prior preference basis) public collegecan increase its choice probability from 13.3 to54.3 percent by offering $5,000 of no-need aid.As in other examples described here and in Chap-ter 4, it appears that relatively large amounts ofmoney are required to induce substantial changesin choice probabilities.

Additional implicit trade-offs and choice scen-arios. Chapter 4 contains extensive discussion ofthe implicit trade-offs made by high ability stu-dents in their college choice decision making.Also, other choice scenarios are examined to il-lustrate the application of the empirical findings.

Determinants offinancial aid awardsThe 1,183 students with whom interviews werecompleted in this study received a total of 3,988admissions offers. Of the 1,183 students, 754 (64

a 7

3

Table 1.2. Illustrative probabilitiesPs)bahility of choosing college A. if ciollege A offers the following amounts ofno-need scholarship aid$0 $1.000 $2.000 $3.000 $4.000 $5.000

If colleges A and B areequally preferred on aprior preference basis

42.8 53.2 63.0 71.9 79.3 85.2

If college A is the first-choice prior preferencecollege

78.4 84.6 89.2 92.5 94.9 96.5

If crllege A is the second-choice prior preferencecollege

13.3 19.0 26.0 34.5 34.2 54.3

percent) received at least one offer of financialaid. Of the 3,988 admission offers, 1,486 (37 per-cent) were accompanied by an offer of financialaid. The extent to which these financial aid offerswere based on academic considerations can beestimated in several ways.

Students offered financial aid wcre asked dur-ing telephone interviews whether any of the offersthey received were based in whole or in part onacademic considerations. A total of 572 of thesehigh-ability students (48 percent of the sampleand 76 percent of those offered any aid) indicatedhaving receive.! aid offers based at least in parton academic criteria. Use of no-need criteria wasalso evident in 'he number of aid offers to stu-dents who had nc:. applied for aid. Of the 3,988admissions offers, 1,659 were to students whohad not applied for aid at the college offeringadmission. About 14 percent of these 1,659 non-aid applicants actually received financial aid of-fers from colleges.

Data available for individuals in the sample(including measures of family financial circum-stances and academic ability), as well as dataavailable for colleges offering admission and aidto these students, permitted development of sta-tistical models to account for the incidence andamounts of aid awards in terms of both individual

and institutional factors. Several main conclu-sions were supported by these analyses.

With regard to the incidence of financial aidawards to students who applied for aid:

Incidence of aid awards (the probability that astudent will be offered any aid) was dnterminedprimarily by financial need (college costs in re-lation to expected family contribution) for stu-dents offered admission at colleges ranking high-est on a proxy measure of academic reputation.

Academic ability played a stronger role thanfinancial need in determining whether or not aidapplicants would be offered any aid by collegesranking below the top 80 colleges on the measureof academic reputation.

With regard to the incidence of financial aidawards to students who did not apply for aid:

Students reported receiving aid offers for whichthey had not applied from colleges with highranks on the reputation measure as well as fromthose with lower ranks. However, such offerswere made far more often by lower-ranking thanby higher-ranking colleges.

For both high- and low-ranking colleges, aca-demic ability as measured by SAT scores wasstrongly associated with offers of aid to studentsnot applying for it.

With regard to amounts of aid:

1 4 8

Over 20 percent of aid offers reported hy stu-dents exceeded "need," defined here as the dif-ference between total college costs and expectedfamily contribution calculated by the CollegeBoard's College Scholarship Service. There are anumber of reasons why aid awards may exceed"need" calculated in this way, since institutionsuse a larger body of information about applicantsin determining aid awards. We found, however,that for both high- and low-ranking groups of col-leges on the academic reputation measure, thechances of a student receiving an aid offer ex-ceeding need (as defined above) increased mark-edly with increasing SAT scores. Thus, theamount of aid awards appears to be, in part, afunction of students' standing with respect to ac-ademic criteria.

It should be noted that in the analyses leadingto the above conclusions, colleges were groupedon an academic reputation measure. Thus, theseconclusions apply in an aggregate sense to col-leges belonging to different groups. Individualcolleges may well have financial aid policies andpractices different from those characteristic oftheir groups. and thus these conclusions cannotbe assumed to apply to any given institution.

In sum, the results of our analyses of aid offersappear to be highly consistent with other infor-mation on allocation of discretionary aid by insti-tutions. Colleges in our highest-ranking group onan index of academic quality (ores which alsoattracted a highly disproportionate share of ap-plications from students in our sample) appear tobe more responsive to need than to academic"merit" in determining whether to offer financialaid to admitted high-ability students. Collegesranking lower on our academic quality index(ones that are at a disadvantage in competing forable students) appear to be offering no-need aidwith greater frequency to able students. Whilethese differences among college groups were ev-ident from our data, it was also apparent that atleast some of the higher-ranking colleges were

responding to academic criteria in determiningamounts of aid awards and in offering aid to stu-dents not applying for it.

Chapter 5 describes in detail the empirical find-ings with regard to financial aid incidence anddeterminants.

Antecedents of choice behavior:Preference and perceptionformationGiven the paramount importance of prior prefer-ence in college choice decision-making behavior,the natural question arises as to the determinantsof prior preference. Our results indicate that per-ceived college academic quality is the main de-terminant of prior preferences for colleges. Inturn, the main influencer of perceived collegequality is actual college quality, as proxied by anindex formed from a number of objectively veri-fiable college quality measures.

Prior preference for a college is principally in-fluenced by a student's perceptions of the col-lege's academic quality. Our composite academicquality perception index included such underly-ing perception rating scales as "academic facili-ties," "overall academic reputation," "availabilityof special majors, degrees, or honors programs,""preparation for career or graduate and profes-sional school opportunities," and "academicstrength in your major areas of interest." A stu-dent's perceptions of a college's lifestyle, qualityof personal contact, and location are secondarybut importantfactors involved in the collegepreference judgment formation process.

Actual college quality is the primary determi-nant of students' perceptions of academic quality.Other interpretable a, statistically significantlinkages exist between a college's objectively ver-ifiable characteristics and students' perceptionsof academic quality, lifestyle, quality of personalcontact, and location. These linkages are de-scribed in Chapter 7.

9

1 5

Chapters 6 and 7 describe in detail the empir-ical findings with regard to the determinants ofthe antecedents of choice behaviorpreferencejudgment formation and perception formation.

Other factors influencingcollege choice behaviorThe role, incidence, and influence of campus vis-its and post-admissions contacts are analyzed inChapter 8. Main findings include a high corre-spondence between campus visits and studentchoice behavior, the infrequent incidence of post-admissions contacts of any kind, and the gener-ally positive impact of all kinds of post-admis-sions contacts. The source of the contact (e.g..admissions representative versus faculty mem-ber) does not seem to matter: all contacts aregenerally viewed as being either positive or neu-tral, with very few contacts being reported asnegativdy influencing students' views of colleges.These results suggest that careful and thoughtfulmanagement of such post-admissions contact ac-tivities is desirable.

Changes in college plans afterinitial decisionsA follow-up survey of our sample in the fall of1984 found that 98 percent of respondents en-rolled in the colleges they indicated as their orig-inal choices in an earlier survey stage. For stu-dents applying to only one college, earlier choiceswere assumed to be the single colleges listed onthe mail questionnaire. For other students, initialchoices were determined in the telephone inter-viewing phase. About 1 percent of the respon-dents to the follow-up survey did not enroll in anycollege in the fall of 1984 and an additional 1percent enrolled in colleges other than the onesinitially named in the mail and telephone sur-veys.

This very high degree of congruence between

1. 6

choices reported in the spring and fall attendancewas unexpecti in view of reports of admissionsofficers concern..:g "no-shows--students whodefer choices by accepting admissions offers frommultiple colleges. We believe that our findingscan be attributed largely to the timing and pro-cedures of our telephone interviews, in whichcallbacks were made into mid-to-late June to un-decided students. Although a sizable minority ofstudents accepted to selective colleges appear todefer choices past the beginning of May, it ap-pears that stable choices have been reached bynearly all students by late June.

The details ail,' results of this follow-up studycomponent a-e ors.2ribed in Chapter 9.

Concluding remarksOur results indicate that most colleges attend toa student's academic ability in determiningwhether a student receives financial aid and thesize of the aid package. Furthermore, monetaryconsiderations are important to students whenthey choose among colleges to which they havebeen admitted. However, the influence of moneyis relatively modest compared to other factors.The primary determinant of college choice is per-ceived college quality, which is demonstrated tobe related to a range of objectively verifiable qual-ity measures.

Further researfth is needed in the area of col-lege search behavior. In particular, a detailed in-vestigation of the determinants of application setformation behavior would shed considerable lighton the role of costs and money in leading to acollege being included in or excluded from theapplication set. Since any college excluded froma student's application set has no chance of beingchosen, colleges obviously must attend to the de-terminants of this crucial decision in the collegeselection process.

2. A comprehensive model ofcollege choice behavior:Theory and measurementPrevious researchers have studied college choicefrom a number of perspectives. Varying view-points naturally result in attention being directedto different sets of factors and variables thatmight influence college choice. The range of var-iables studied at one time or another includesstudent characteristics and background, studentattitudes, student perceptions of colleges, collegecharacteristics, money (parental income level,tuition, and financial aid), student self-reportedpreferences, and actual college choices of stu-dents.

In this chapter, we will develop a theoreticalmodel of college choice behavior that is meant tobe comprehensive, in the sense that it encom-passes and accounts for all of these various con-siderations and their interrelationships. Thismodel decomposes the college choice processinto a series of interrelated stages, each compo-nent of which may be examined separately usingwell-established statistical analysis procedures.In conceptual terms, our theoretical collegechoice model v:ews students as forming inter-mediate summary measures to describe variouscollege options and then evaluating the collegesby weighing these intermediate constructs. Weseek to analyze which intermediate summarymeasures are used by students, how these mea-

sures are weighed in forming college choice de-cisions, and how these measures are related toand determined by actual observable character-istics of colleges (and other factors).

This multistage model is an extension of a well-established model of buyer behavior in market-ing, the perception-preference-choice model (Ur-ban and Hauser 1980; Hauser, Tybout, and Kop-pelman 1981; Tybout and Hauser 1981). Similarmodeling efforts may be traced back to the lensmodel (Brunswik 1952). Information integrationtheory (Anderson 1974, 1981, 1982) provides asimilar multistage perspective on complex judg-ment and evaluation processes, such as the col-lege choice process.

Preliminary remarksIt is desirable to begin by noting several defini-tions that will be used in developing this compre-hensive multistage model of college choice be-havior.

College search and choice behaviorThe college selection process is composed of twogeneral phases: college search and college choice.For our purposes, "search" will be deemed tohave ended when a student submits applicationsto a set of colleges. After the colleges make theiradmissions decisions, the "choice" phase begins.Choice is, by definition, the process by whichstudents choose a single college to attend from

among those to which they have been admitted.For choice to occur, a student must have beenadmitted to at least two colleges. (Students whoapply to only a single institution have made im-portant college selection decisions within the col-lege search phase. As such, these students wouldbe beyond the scope of the current study. sincesearch behavior is not analyzed here.)

In studying choice, it may be implicitly as-sumed that all colleges being considered are atleast minimally satisfactory on all major dimen-sions of choice; otherwise, they presumablywould have been screened out during the earliersearch phase. (This is not true for the cost di-mension, since the complete costs associatedwith attending a particular college are not knownto the student until after a college's financial aiddecision has been made and communicated.)Thus, a compensatory or trade-off model of be-havior seems viable here. In such a compensatorymodeling framework, a student is implicitlyviewed as weighing the various considerations as-sociated with college choice and trading off lesserperformance on some dimensions for greater per-formance on others.

Application set formationand choice behaviorIn studying choice behavior, we assume that theapplication set of colleges has already beenformed. We propose to study only the later stagesof college selection: college choice behavior.Thus, we are unable to examine how search ef-forts may have influenced and shaped the ulti-mate college choice outcome.

This limitation in studying college choice be-havior is important. It may lead to apparentlyanomalous results. For example, it is possiblethat distance (from a college's campus to a stu-dent's residence) may turn out to be an irrelevantfactor at the level of college choice. This wouldseem to fly in the face of the empirical "fact.'

.18

that most students attend colleges near theirhomes. This apparent anomaly may be resolvedby noting that such a distance factor. if it exists,presumably has a major bearing on the set ofcolleges to which a student applies. Since all col-leges in a student's application set are likely tobe minimally acceptable on the distance dimen-sion. finding that distance is irrelevant at the levelof choice is. indeed. possible. Such a finding re-sults from the major screening influence that thesearch and application formation set decision pro-cesses exert on the college choice process.

Costs represent a second potential example ofhow the oarlier processes of college search andapplication may influence choice behavior studyfindings. In analyzing choice behavior (as definedabove), we may find that costs are of secondaryimportance to other factors. This finding mightresult because colleges that are perceived by thestudents (or their parents) to be too costly arescreened out at the application formation stage,so that choice ultimately revolves around collegeswhich are minimally acceptable on the cost di-mension. One counterargument regarding thiscost finding is that students do not know theircomplete costs when they apply to colleges, sincethe financial aid packages are not known until theadmissions and aid offers are communicated bythe college to the student. Students may. ofcourse, form expectations as to their financial aidawards and, thus, their net costs.

Individual differencesIndividual differences may arise in two ways inthis model of college choice behavior: differentkinds of students may perceive the world differ-ently or students may value what they perceivedifferentially. Here, "different kinds- of studentswould be described by demographic, attitudinal,and other background variables.

In studying individual differences, we seek toexpand upon the work of Chapman (1979), whose

12

Preferencej

study of college choice behavior uncovered someimportant differences across different studentsegments, where the segments were defined interms of students' planned academic field ofstudy (engineering and science, liberal arts, andfine arts) and in terms of parental income levels.In this empirical effort, we wish to be sensitiveto the possibility that important individual differ-ences may exist.

In this study. we introduce another aspect ofindividual differences Li the study of collegechoice behavior: context effects. For example,students choosing between high-priced private in-stitutions only and, alternatively, among high-priced private institutions and a local public in-stitution are expected to exhibit different choiceprocesses. Costs for the former group arepresumably less important than for the lattergroup. Our college choice model and empiricalanalyses are designed to be sensitive to assessingthe presence of such choice-context individualdifference effects.

An overview of a multistage modelThe organization of our multistage model of col-lege choice behavior is depicted in Figure 2.1.The three main components of this model de-scribe the interrelationships between perceptionjudgment formation. preference judgment for-mation, and choice behavior.

Students are presumed to form perceptions ofcolleges based on the actual physical (objectivelyverifiable) attributes/characteristics of the col-leges and on the information they possess abouta college. Here, "information" includes both thesource of the information and its content. Sinceany finite set of college attributes may not easilybe able to capture all aspects of perception, thepresence of colleg,specific ("brand name") influ-ences on perceptions Dre postulated. Finally, in-dividual differences may cxist, in that certain stu-

Perceptions

CollegeCharacteristics

SituationalConstraints

InformationEnvironment

0

A

A

Figure 2.1. A multistage model of college-choice behavior

dent groups may perceive colleges differently orweigh their perceptions differentially.

The process by which students evaluate col-leges is split into two parts in our multi-stagemodel: preference formation and choice behavior.This is done for several reasons. We wish to re-serve the treatment of financial considerations forthe choice phase. Also, we wish to ignore, for themoment, the ccfistrained nature of choice, in thata student may choose only from among those

colleges who admitted him or her. Thus, in thepreference phase, we wish to have students re-port on their preferences for college alternativesunder the assumptions that money was irrelevantand that they v re admittee to all colleges towhich they applied. One final differentiating fea-ture between the unconstrained preference andchoice phases may be noted: unconstrained pref-erences are self-reported by the students, whilechoice refers to actual student behavior.

The splitting of the college evaluation processinto two parts is done primarily to isolate thefinancial aid and cost considerations (classified asbeing among the situational constraints in thismodel) in the college choice process. By includEngmost factors other than money in the preferencestage, it is expected that it will be easier to iden-tify the role that financial considerations play incollege choice behavior.

Analysis at the choice phase is based on re-vealed preference behavior. Actual college choiceis observed, and we wish to infer the relativeimportances of unconstrained preferences andsituational constraintssuch as financial consid-erations (costs and financial aid)on choice be-havior. As always, individual differences may ex-ist here. Income levels (relative to college costs)are perhaps the most important individual differ-ence possibility to be explored.

We now turn to discussing the perception, pref-erence, and choice phases in more detail. Datarequirements, measurement issues, operational-ization, and estimation approaches are exploredfully in the following sections of this chapter.

Perception judgment formationIn the perception judgment formation stage, weseek to model the process by which college per-ceptions are formed. We postulate that a stu-dent's perception of a college depends on theactual physical (objectively verifiable) character-

istics of a college (e.g., size); objectively verifiableinteraciions between the student and the college(e.g., the distance from the student's residenceto the college's campus); college-specific effectsnot otherwise captured by a college's physicalattributes (e.g., "brand name" effects); and theinformation the student possesses about the col-lege, including the source and content of thatinformation. It is presumed that this linkage be-tween how the world actually is (the objectivelyverifiable attributes of the colleges) and how it isperceived (the self-reported perceptual-ratingscales) exists, although we are likely to have con-siderably less than perfect success in such a sta-tistical modeling exercise due to the inevitablefallibility of our rating-scale measures and ourinability to include all possible determinants ofperceptions in any statistical model.

In mathematical terms, this may be expressedas follows:

Rd e,rce,CSErpl se(!) (1)

where

Rsrd

X,

CSE,

a studenta collegea perceptual dimensionthe perceptual rating (score) student s gives tocollege c along perceptual dimension d (for d= 1,2,-the physical (objectively verifiable) attributesfor college cthe physical (objectively verifiable) interac-tions between student s and college ca college-specific effect for college c: the dis-tinctive brand-image of college c which is notadequately captured by the perceptual-ratingvariablesthe information student s possesses (and thecorresponding information sources consultedby student s) about college c on dimension d.

College attributes, or characteristics, includeboth academic and nonacademic features. Aca-

20 14

demic dimensions of interest would include thequality of the academic enterprise plus thebreadth of course/major/program offerings. Un-der the nonacademic category, a range of life-style considerations would merit attention. Extra-curricular activities, diversity of student body,and campus location are but three of the potentialnonacademic features to which students may di-rect their attention when choosing among col-leges.

Parental educational background and distance(from a campus to a student's residence) arepotential individualinstitution interactions ofnote. If a parent attended a cohege, this extrainformation source might influence a student'sperception of a college (positively or negatively).Distance may influence perceptions negatively.since it may act as a surrogate for uncertainty asto where a college really stands on a perceptualdimension. Of course, the college search phasepresumably is focused on sorting out these kindsof uncertainties.

College-specific effects may exist in the per-ception formation stage. Any finite set of collegeattribute measures may not fully capture all thedistinctiveness of a specific college. It may benecessary to include collcge-specific indicatorvariables to measure the incremental influence ofthe college, above and beyond that which is cap-tured by the other independent variables.

Information possessed and information sourcesconsulted by students about specific colleges areparticularly difficult aspects of perception for-mation to measure in the context of a study ofcollege choice. Since the college choice processbegins at the point at which the application set isformed, there is a delicate problem concerningdirection of causality. Are perceptual scoresreally a function of informationas our modelpostulatesor are self-reports on informationcontent formulated to reflect perceptual scores?It would appear that the disentangling of these

effects would require measures of the informationcomponent of the perception process at a stageor stages earlier than when the application set isformed.

In estimating the model in equation (1). it isimportant to note that the simple regression ofthe independent variables on a raw ratings-scalemeasure makes a very strong assumptionnamely, that the students' choice sets all consistof more or less the same college alternatives.Furthermore, such a regression-modeling ap-proach presumes that the students use approxi-mately the same standards for rating colleges.That is, they are assumed to use the same ratingsscale for deciding on when a college is "excel-lent" versus when it is only "good." More sophis-ticated model forms may be required to capturethe relativeness inherent in the reporting of per-ceptions. The essence of perceptual ratings isrelativenfs, not absoluteness. Since perceptualratings scales are only relative themselves, choiceof a model form for the perception formationstage must take this consideration into account.

To combat this potential ratings-scale hetero-geneity problem, oy- analysis approach will in-clude standardizing the ratings of the college foreach student prior to estimation of the perceptionjudgment formation model. Such within-respon-dent standardizations are recommended in anal-yses such as this one (cf. Dillon, Frederick, andTangpanichdee 1985).

?reference judgment formationPreference, as used here, denotes the overallevaluation jf the worth of a college alternativefrom the point of view of a student. Preference ispostulated to depend on perceptions. In addition,constrained preferences are presumed to depcndon individual-institution interactions and col-lege-specific influences. Unconstr ined prefer-ence considers all factors except financial ones,

15

21

which are reserved for treatment at the choicephase due to their inclusion among the situationalconstraints facing a student.

The general form of the preference judgmentformation process is as follows:UPP =

UPPIR1. .1?,i. . RD:Y,:C.SE,) (2)

where

UPP

CSE,

a studenta collegethe unconstrained prior preference probabilityof student s for college cthe perceptual rating of college c by student son dimension d (for d = 1.2.. .D)the individualinstitution variables which re-late student s and college ca college-specific effect for college c: the dis-tinctive brand-image of college c which is notadequately captured by the perceptual ratingsvariables (an indicator variable for college c.which equals 1 for college c and zero other-wise).

The perceptual views of the student are pre-sumably the major determinants of preference.Students are viewed as forming preferences (val-ues) about colleges based on how they perceivethe colleges. That is, judgments about the worldare viewed as depending on how the world is seen(perceived). For reasons of parsimony, it may beappropriate to combine raw perceptual variablesinto composite indices at the statistical-modelingstage.

Among the relevant individualinstitution in-teractions at the preference judgment formationstage, special familiarity effects and distance mayplay significant roles. Special familiarity effectsinclude whether either parent of a student at-tended a college. It is pi esumed that such legacyeffects result in a net positive influence on stu-dents' inclinations toward such colleges. Distance(from a student's residence to a college campus)may influeace students either positively or nega-

tively. Greater distance represents more separa-tion from family and friends and also has costcomponents associated with it. These factors sug-gest that more distance may be judged negatively.On the other hand, distance may be positivelyperceived since, holding everything else con-stant, high school seniors may wish to see newplaces and experience new parts of the country.These desires may be fulfilled by traveling somedistance from home to attend college.

The college-specific effects are included in thepreference judgment formation model to accountfor the inevitable measurement errors in the per-ceptual ratings. These variables will account fornotable individual college effects that are not fullycaptured in any finite set of fallible perceptualratings.

Since preference is a relative construct, a sta-tistical model that explicitly takes relativenessinto account is required. The multinomial logitmodel will be adopted here. This model is de-scribed in detail in Appendix 1.

Choice behaviorThe variables of interest at the choice behaviorstage include unconstrained preference probabil-ities, financial considerations, other situationalconstraints, and post-admissions contacts.

The general form of the choice model is asfollows:

PC, = PC(UPP,.M.CSEc.PAC,.SC,) (3)

where

22 16

s a studentc a college

PC, the probability that student s will choose toattend college c

UPP the unconstrained prior preference proba-bility of student s for college c

/11. the money variablescosts (tuition, roomand board, and other expenses). financial aid

(scho) 'hips, loans, and part-time jobs), andparenta; incomerelating individual s andcollege c

CSE, a college-specific effect for college c: thedistine.4ve brand-image of college c which isnot ad-iquately captured by the uncon-strained prior preference probability (an in-dicator variable for college c, equals for col-lege c and zero otherwise).

PAC post-admissions contacts (by letter, by tele-phone, and in person) of college c with stu-dent s

SC situational constraints which affect students when considering the choice of college c.

UPP (unconstrained prior preference probabil-ity) plays a crucial role in this choice behaviorcomponent of the multistage college choicemodel. It is meant to summarize all the variables,and their associated effects, described in thepreference judgment formation phase. By includ-ing UPP in the choice behavior component, allthe variables in the preference judgment forma-tion phase do nat have to be included here. Thisleads to a substantially simpler model form withconsiderably fewer variables, less co-linearityacross variables, and correspondingly easierinterpretation of the resulting relative-importanceweights. UPP is, of course, expected to have amajor influence on choice behavior.

UPP, the unconstrained prior preference prob-ability, would be estimated using the model inequation (2). An alternative operationalization forUPP might involve using several indicator vari-ables representing whether an alternative was afirst, second, or third choice, for example, at theprior preference stage.

One obvious situational constraint is the com-position of the choice set itself. Students maychoose only to attend colleges to which', hey havebeen admitted. Financial consideratiun.; repre-sent another kind of situational eonstra:nt. Mon-etary considerations include gross costs of at-tending a college (tuition, room and board, and

other expenses) and financial aid offered by acollege (scholarships, loans, and part-time jobs).The influence of income level may be an impor-tant individual-difference aspect.

Once again, college-specific effects. proxied bycollege-specific indicator variables. may be pres-ent in the choiee stage. These "brand name-effects may not have been fully captured by theunconstrained prior preference probability mea-sui.es.

Post-admissions contacts initiated by a collegemay have an influence on students' behavior, andthe effects of such contacts will not, by definition,have been captured in the unconstrained priorpreference judgments. Estimation of the influ-ence of post-admissions contacts depends cru-cially on knowing who initiated a contact: thestudent or the college. A direction-of-causalityproblem arises if the student was the initiator. Insuch a case, it is impossible to determine with asingle post-choice question of contact incidencewhether the student's interest resulted in the ini-tiation of the contact or the contact changed thestudent's interest level in a college. Campus visitsare perhaps the most visible of the post-admis-sions contact activities. (See Chapter 8 for someresults related to the incidence and influence ofcampus visits and post-admissions contacts.)

Since choice involves choosing among a finiteset of alternatives, relativeness of choice is para-mount. Our goal is to estimate the relativeimportance of unconstrained prior preferenceprobability, money, college-specific effects, andpost-admissions contacts on final college choicebehavior. We will adopt the multinomial logitmodel form to estimate the relative importancesof these factors, as revealed by students' actualchoice behavior. This widely used brand choicemodel permits quantitative estimates of the rela-tive importance parameters to be derived. In ad-dition, the model form permits detailed policyanalysis and assessment to answer questions re-

17,

23

lated to how choice probabilities are influenced bychanges in financial aid. This multinomial logitmodel is described in Appendix 1.

Other approaches to studyingcollege choice behavior'Single-stage versions of this multistage college-choice model have been developed by previousresearchers (see, for example, Kohn, Manski, andMundel (1976); Chapman (1977, 1979); Punj andStaelin (1978); and Manski and Wise (1983). Themost famous study in the college choice domainis undoubtedly the Manski and Wise (1983) effortusing data from the National Longitudinal Studyof 1972. The scope of their study and the ad-vanced statistical modeling tools brought to bearin studying college-going and college choice be-havior are particularly notable.

Manski and Wise's choice model was a single-stage one of the form

choice = f (college attributes, money,other factors).

Thus, the possibility of perceptual distortionscould not be detected. The size of their data basepermitted the exploration of the presence of in-dividual differences in a limited way, with refer-ence to demographic variables only. Also, Manskiand Wise had only limited financial aid informa-tion (for the college to which the student matric-ulated). They had to statistically impute financialaid offers of competing colleges.

While our study seeks to investigate some ofthe same questions of interest, it represents anumber of important advances over Manski andWise. First, the quality of our data is excellent,particularly with regard to financial aid informa-

1. The remaining sections of this chapter deal primarily witha variety of methodological issues associated with collegechoice and enrollment research. These sections are not es-sential to an understanding of the reseal Ai findings presentedlater in this report.

24

tion. Second, our data reflect recent collegechoice behavior and the financial aid awardingbehavior of colleges. Third, our college choicemodeling framework is considerably richer thanthat of Manski and Wise. Our model is a muchmore gimeral version of their single-stage choicemodel. While a multistage model has substan-tially greater data collection and estimation costsa..3ociated with it, the potential bellefitsinterms of greater understanding of the forceswhich operate during the college choice pro-cessare substantial.

Methodological considerationsin estimating relative-importanceweightsThe three components of the college choicemodelperception formation, preference judg-ment formation, and choice behaviorinvolve es-timating relative-importance weights: what con-siderations are important and how important theyare. These relative importances describe how anumber of variables are related to perceptions,preferences, and choices. Two kinds of ap-proaches exist for establishing such relative im-portances: self-reported weighting proceduresand statistically derived weighting procedures.

Self-reported weighting proceduresSelf-reported weighting procedures involve ask-ing survey respondents to report ("self-estimate")how important various factors are to them in somedecision-making, evaluation, or judgment con-text. Sometime; respondents are asked to iden-tify the most important considerations from alengthy list of possibilities. These multifactor rat-ing tasks have a long history in marketing andsurvey research. For example, a number of per-ceptual dimensions might be described and therespondents might be asked to rate the relativeimportance of each in the context of choosing acollege.

18

A major advantage of such self-reportedweights is that they are individual-specific. Suchself-reported weights are gathered at the level ofan individual respondent, thus explicitly acknowl-edging the possibility of individual differences(respondent heterogeneity). A second major ad-vantage associated with such weighting proce-dures is ease of measurement and analysis. Theresearcher has only to develop a list of potentialfactors that might be relevant in a choice situa-tion, by using exploratory research techniquesand by scanning the existing published literature,and then display the list to respondents. Simplearithmetic means of the scales or percentages ofmost frequently chosen factors suffice to sum-marize the results.

Some serious problems exist, however, in usingself-reported weights in complex decision-makingand evalultion processes, like college choice. Re-

spondents may not know their own relative-importance weights, or they may not be able toeasily articulate their weights during a survey.Respondents may report that everything is im-portant, thus defeating the purpose of estimatingsuch weights: to determine the trade-offs thatdecision makers are prepared to make. Finally,such self-reported weights do not lend themselvesto policy analysis questions, such as how changesin financial aid might influence choice probabili-ties (actual enrollment behavior).

Some self-reported relative-importance resultsfrom a large ongoing survey of students (Astin etal. 1983, 1984, 1985) are reported in Table 2.1.As may be noted, college-quality considerations("has a good academic reputation," "graduatesget good jobs," and "graduates go to top gradschools") dominate the results, holding down thetop three positions. Financial considerations are

Table 2.1. The determinants of college choice behavior: An example ofself-reported importance considerations from the published literature

Reason

Percentage reporting the reason as very important inchoosing the college that v.as selected

1983 1984 1985

Has a good academic reputation 49 52 55Graduates get good jobs 44 44Graduates go to top grad schools 24 25 26Has low tuition 20 20 21Has a good social reputation 20 21 23Offered financial assistance 19 18 20Offers special education program 18 18 22Wanted to live near home 17 16 18Advice of guidance counselor 8 8 8Friend suggested attending 6 7 7Athletic department recruited me 6 6 5Relatives wanted me to attend 6 6 6Teacher advised me 4 4 4Not offered aid by iust choice n/a 4 4College rep recruited me 3 3 4

Source: Astin et I. (1983. 1984. 1985).

19

25

the fourth and sixth highest-rated considerations("has low tuition" and "offered financial assis-tance"). These ratings appear to have remainedquite stable from 1983 through 1985.

In attempting to make use of such self-reportedrelative-importance weights, the admissions andfinancial aid planner has received only some di-rectional information. It is not possible to usesuch ratings data to determine, for example, howmuch financial aid might offset a less desirableacademic quality evaluation. More precise andsophisticated statistical modeling and analysis isrequired to address such questions.

Statistical weighting proceduresStatistically derived weighting procedures involveestimating the relative-importance weights usingstatistical procedures. Rather than using self-reported weights, the weights are statistically de-termined to be maximally consistent with someobserved (behavioral) phenomena. Thus, for ex-ample, we observe students actually choosingcertain colleges from sets of specific colleges towhich they are admitted. Based on these ob-served choices, we then attempt to work back-ward and to infer how some variables describingthe choice alternatives (e.g., college luality orfinancial considerations) were implicitly weighedby the students in arriving at their actual ob-served final choices.

In the college choice domain, the multinomiallogit model has been used extensively to analyzethe forces which influence college choice behav-ior (see Kohn, Manski, and Mundel 1976; Chap-man 1977, 1979; Punj and Staelin 1978; and Man-ski and Wise 1983 for examples). By using formalstatistical models in connection with a statisti-cally derived weighting procedure, it is possibleto provide a mechanism for assessing the quan-titative trade-offs that students implicitly makebetween, say, college quality and financial con-siderations.

2 6

Statistically derived weighting procedures aretypically based o. pooling a number of surveyrespondents' data. thereby implicitly assuminghomogeneity of the relative importances acrossthe pooled survey respondents. It is necessary tobe sensitive to the possibility of. and to statisti-cally test for, respondent heterogeneit,. Simplepooling tests exist for performing such assess-ments (e.g.. see Chapman and Staelin )982 andalso the discussion in Appendix 1).

The multinomial logit model is 7ised in thisstudy to estimate the relative-importance weightsfor college choice behavior and prior preferenceformation. See Appendix 1 for an overview ofsome key aspects and features of the multinomiallogit model.

Data r:ollectionfor a multistage modelThis multistage model of college choice behaviorhas much more extensive data requirements thanthe typical matriculant and admitted applicantsurveys with which college admissions officialsare familiar. Some remarks comparing the mul-tistage: model and typical matriculant and admit-ted applicant surveys seem appropriate.

The most inexpensive form of research on col-lege choice behavior would be a matriculant sur-vey. In such a survey, a college might survey itsmatriculants once they have arrived there. Ma-triculant surveys are quick and inexpensive toconduct, especially if they are administered in amass fashion, perhaps during an on-campus ori-entation period at the commencement of classes.However, the data derived from such surveys areof extremely questionable quality. The surveysare conducted too long after the actual collegechoice decisions were made, so memory lapsesand faulty recall are likely to be serious impedi-ments to "clean" data collection. Also, cognitivedissonance (self-rationalization) considerations

20

suggested that self-reported weights and collegeperceptions may be severely contaminated. Fi-nally, there is a serious sampling problem in ma-triculant surveys: only the students who chose acollege are included. The students who rejectedthe college are not included in the population forcomparison purposes.

An admitted applicant survey corrects the sam-pling bias problem inherent in matriculant sur-veys. In admitted applicant surveys, all of a col-lege's admitted applicants are contacted, thusresulting in the inclusion of both matriculants andnonmatriculants in the study population. The sin-gle contact point for such admitted applicant sur-veys is typically between late April and earlyJune, after the choice decision has been made butwell before students actually enroll at the chosencolleges. Some problems, however, continue to ex-ist with admitted applicant surveys. First, suchstudies are typically done by individual colleges,and the findings usually are not publicized due tocompetitive considerations. Second, since col-leges survey only their own admitted applicantpool, even if the study results were made public,issues related to generalizability would arise.Third, a single postchoice retrospective surveymay encounter considerable problems with mem-ory lapses, faulty recall, and postchoice rational-izations (of the form "I'm going to the college, soI must like it"). Fourth, issues of direction-of-cau-sality arise between perceptual ratings and pref-erence/choice: is preference/choice a function ofperceptual ratings, or is it the other way around?Such issues cannot be resolved with a single-stagesurveying effort which asks respondents to pro-vide both ratings of colleges' performance/stand-ing on a number of dimensions and overall rank-ings of the colleges rated.

Our multistage model of college choice behav-ior requires that data be collected at more thanone point during the choice process. In particular,data on perceptual ratings and preferences must

be collected before a student learns of admissionsand financial aid decisions, and before actual col-lege choices occur. A second wave of data collec-tion is necessary after the final college choice ismade, in the style of an admitted applicant sur-vey. However, this second wave focuses only onmeasuring the actual college choice, the compo-sition of the choice set (the colleges to which thestudent was ultimately admitted), and the finan-cial aid awards made to the student by all collegesto which he or she was admitted. In addition, tosatisfy the requirements of generalizability, thestudy population must be all high school students,not just the applicants (admitted or otherwise) toa particular college or group of colleges. With thesupport of the College Board, we were able touse SAT takers as the population. These consid-erations guided the data collection effort, whichis described in Chapter 3.

College choice modeling andadmissions yield ratesTo further indicate how our statistical model ofcollege choice behavior relates to typical admis-sions and financial aid research efforts of individ-ual colleges, we may note that yield rates are ofconsiderable interest to those who manage as-pects of the admissions and financial aid pro-cesses. Such yield rates typically are calculatedin selected pairwise competitive situations andinvolve examining the actual outcomes in overlapadmissions situations. For example, if 100 stu-dents were admitted to both colleges A and B,and 40 of these students ultimately chose to at-tend college A, then college A's yield rate is 40%in competition with college B. (Note that collegeB's yield rate might be 35 percent, the remainingyield accruing to other colleges that were notincluded in the pairwise overlap admission be-tween colleges A and B.) An admitted applicantsurvey provides the necessary data to estimate

2 7

Table 2.2. Some national norms for enrollment success rates(yield-rate percentages)

National

Regional breakdown

Smo h Nlidwest Snuthwest West

NewEngland

MiddleStates

Four-year publiccollegesFall 1982 57.9 47.1 45.2 63.5 59.5 67.8 64.7Fall 1983 56.3 53.8 43.3 60.5 58.3 69.4 58.8Four-year privatecollegesFall 1982 48.0 41.7 46.3 51.0 50.8 64.4 1.8.7Fall 1983 47.9 42.1 45.3 50.3 51.6 66.8 18.6

Source: College Entrance Examination Board. Annual Survey of Colleges 1984-85: Summary Statistics (M,

such yield rates. Necessary data include appli-cation set composition information, admissionsdecision outcomes for each college in a student'sapplication set, and the student's final collegechoice.

Aggregate yield rate is the percentage of alladmitted students who attend a college. Somenorms for aggregate yield-rate data across variouscollege segments are displayed in Table 2.2.

Our statistical modeling efforts are designed toattempt to explain the determinants of such yieldrates. We seek to determine, in particular, how

28

financial aid and other factors (such as collegequality) influence college choiceswhich, whenaggregated across a group of students, becomeyield rates. A yield rate is, after all, only an ag-gregate statistical summary measure. Admissionsand financial aid planners require information onhow they might be able to influence yield rates ifthey are to cope with the many demands associ-ated with thoughtful, efficient, and effecti%, ad-missions and financial aid decision making andplanning.

22

3. Study design and data collection

The design of the study and the associated datacollection effort followed from the formulation ofthe comprehensive multistage college choicemodel described in the previous chapter. We be-gin this chapter by describing the design of thetwo-stage surveying procedure, the data require-ments, and sources of data for our college choicemodeling effort. Sampling procedures used in thestudy will then be discussed. A nonrespondentbias analysis is conducted and reported. Thechapter concludes with a brief statistical over-view of the student population which comprisesthis study.

Study design, data requirements,and data sourcesThe two-stage surveying procedure adopted inthis study included an initial mail survey and afollow-up telephone survey. The mail survey wasconducted in March 1984, after the students hadformed their application sets but before most ac-tual college choices had been made. The follow-up telephone interviews occurred in May/June1984, after the college choice process had con-cluded. Appendixes 2 and 3, respectively, containthe wording of the questions on the mail andtelephone interview surveys.

The data requirements to estimate the variouscomponents of this comprehensive multistagecollege choice model are described in Table 3.1.

Sai,:pling procedureFor our purposes, we were interested in high-ability high school seniors, since these would bethe students most likely to attract no-need finan-cial aid. In this study, high-ability students weredrawn from the 1983-84 high school graduatingclass. Students were included in our populationif they (1) scored 550 or more on the SAT (averageof verbal and mathematkal scores); (2) were inthe top fifth of their high school class (self-reported on the Student Descriptive Question-naire associated with the SAT); and (3) were U.S.residents.

Based on survey response rates in past collegechoice research efforts, and the requirements forthe statistical analysis in this study, an overallsample size of 2,000 was selected.

A disproportionate stratified random-samplingprocedure was used in this study. Students withaverage (mathematical and verbal) SAT scores inthe ranges 550-599, 600-649, 650-699, 700-749,and 750-800 were sampled with equal frequency.Thus, a total of 400 students were included ineach of these 50-point ranges on the SAT. Theeffects of this disproportionate sampling plan ondepth-of-population strata sampled is describedin Table 3.2. As may be noted, while we sampled/

23

29

Table 3.1. Data requirements and sourcesData requirement Source

Individual student differences:Demographic characteristics, high school ex-periences, and college plansFinancial status variablesStudent SAT scores

Student perceptions of colleges

Student self-reported importance weights

College characteristics

College price data

Unconstrained preferencesFinancial aid awardsPost-admission contactsActual college choices

College Board records: SAT registration andthe SDQ

College Board records: CSS ReportCollege Board recordsMail survey (and telephone survey, for compari-son purposes)Mail questionnaire (and telephone survey, forcomparison purposes)College Board records: The College Handbookdata base (1985 edition)

College Board records: The College Handbookdata base (1985 edition)Mail surveyTelephone surveyTelephone surveyTelephone survey

only 0.9 percent of the students in the 550-599range, our design included 51.1 percent of thestudents in the top SAT group, the 750-800 range.This concentration of sample points in the topSAT ranges was deliberate, since these studentswere most likely to receive large no-need aidawards. Thus, we wish,.d to oversample thesestudents, relative to their natural incidence in the

Table 3.2. Sample sizes in various SATstrataSATscore Strata Sampleinterval size size

% of stratapopulationsampled

550-599 46,504 400 0.9600-649 32,545 400 1.2650-699 16,439 400 2.4700-749 5,331 400 7.5750-800 781 400 51.2

30

population, in order to have ample presence ofsuch financial aid at the analysis stage.

The results of our surveying procedure are de-scribed in Table 3.3. The 77.5 percent responserate to the mail survey is excellent, even giventhe generally high norms (in the 40-60 percentrange) for admitted applicant surveys. Of the1,549 respondents to the mail survey, 325 (21.0percent) applied to only one college (typically un-der an early action, early decision, rolling admis-sion, or similar program). Thus, the eligible pop-ulation for the second-stage telephone survey was1,224. Ultimately, 96.7 percent of these studentsresponded to the follow-up survey. This level ofresponse rate to the telephone follow-up is out-standing, presumably reflecting the attention-get-ting value of telephone interviewing, the timingof the calls (just after the college choice decisionhad been made), and the general interest of thestudents in this study (since they had previouslyprovided information via the mail survey).

24

Nonrespondent bias analysisAlthough the response rates to our surveys wereextraordinarily high-77.5 percent for the mailsurvey and 96.7 percent for the follow-up tele-phone surveyit is still appropriate to conduct anonrespondent bias analysis. Our concern here iswhether the respondents have different charac-teristics than the nonrespondents. Since we haverelevant demographic variables for all 2.000members of our population, the respondents' andnonrespondents' characteristics may be readilyassessed and compared.

Table 3.4 contains a comparison of the mailsurvey respondents and nonrespondents alongfive relevant demographic variables: average SATscore, gender, planned higher educational level,planned field of study, and self-reported parentalgross income. As may be noted, there are nosubstantial deviations between the respondentand nonrespondent groups along any of these de-mographic variables. Thus, these respondentsappear to be representative of the original 2,000students in the population, and a nonresponsebias problem does not appear to be present inthese survey data (at least, based on this com-parison of key demographic variables of the re-spondents and the nonrespondents).

Given the 96.7 percent response rate to thetelephone survey, no formal nonrespondent biasanalysis is necessary. Even if the nonrespondentswere systematically different from the respon-dents, their small number would not materiallyinfluence our results.

Table 3.3. Results of sampling efforts:response rate analysisOriginal sample size 2,000Stage-1 respondents ;mail) 1,5491

Students applying to only one college 325

Eligible population for Stage 2 1.224

Stage-2 respondents (telephone) 1,1832

1. 77.5% response rate. 2. 96.7% response rate.

A statistical overview ofthese studentsThe data reported in Table 3.4 document thebackground of the students in our population. Asummary of the key descriptors would includethe following observations.

The majority of these students are male (63.1percent). In terms of academic field of interest.science (42.2 percent) and engineering (22.5 per-cent) predominate. These high-ability high schoolseniors have high educational aspirations, with76.0 percent reporting graduate-level educationplans. Many of the students come from relativelyaffluent backgrounds (38.2 percent of the stu-dents are from households where the family in-come is $50.000 or more).

Several other aspects of the backgrounds andaccomplishments of these 2,000 high-ability highschool seniors merit mention. These students pri-marily attend public high schools (81.3 percent).They come from family settings where educationappears to be valued and a way of life: 72.4 per-cent (57.4 percent) of their fathers (mothers) havecollege degrees, while 45.8 percent (21.8 percent)of their fathers (mothers) have graduate degrees.With regard to high school athletic participation,79.7 percent of the students competed in sports,with 35.4 percent winning one or more varsityletters. These students were also active in com-munity groups, with 64.4 percent claiming activemembership in such organizations and 24.2 per-cent indicating that they were major office holders.

In summary. these high-ability high school sen-iors are of such ability not only in a narrow aca-demic sense. They appear to be leaders in ath-letic and community groups as well. They alsocome from high-status households. at least asmeasured by parental educational levels and, tosome extent, by household income.

25 31

Table 3.4. Nonresponse bias analysis: Comparisons of demographiccharacteristics of respondents and nonrespondents to the mail surveyDemogxaphic characteristic Total sample Respondents Nonresimndents

Average SAT scores550-599 20.0% 19.0% 23.5%600-649 20.0 19.5 21.7650-699 20.0 19.5 21.7700-749 20.0 20.9 16.9750-800 20.0 21.1 16.2

100.0% 100.0% 100.09

GenderMale 63.1% 62.29 66.3%Female 36.9 37.8 33.7

100.0% 100.0% 100.0%

Planned educational levelGraduate school 76.0% 76.1% 75.9%Bachelor's/uncertain 24.0 23.9 24.1

100.0% 100.0% 100.0%

Planned field of studySciences 42.2% 41.8% 43.6%Engineering 22.5 23.0 20.8Other 35.4 35.2 35.7

100.0% 100.0% 100.0%

Self-reported parentalgross income$30,000 or less 25.9% 25.1% 28.9%$30,001-$49,999 35.9 37.0 32.0$50,000 or more 38.2 37.9 39.0

100.0% 100.0% 100.0%

Note: Due to rounding. some totals do not add up to 100.0%.

3226

4. Determinants ofcollege choice behavior

In this chapter, we report and analyze the resultsof our efforts to assess the determinants of collegechoice behavior. Choice behavior concerns howstudents ultimately choose one of the colleges towhich they have been admitted. In our multistageperception preference choice model, the choicecomponent begins with a prior preference for acollegea measure of college preference uncon-strained by monetary considerations and. othersituational constraints (such as whether a studentwas admitted to a college). This prior preferenceis then attenuated by monetary considerationsand other situational constraints.

Findings related to the choice component of ourmultistage college choice model are presented inthis chapter; findings related to preference andperception judgment formation behavior in Chap-ters 6 and 7. We begin by presenting some de-scriptive statistics concerning the application setformation process. Of particular interest is the re-sult that 21 percent of the students applied only toa single college. Next, we examine the tendencyof students to actually attend their first-preferencecollege and related matters which bear on the col-lege choice decision. Then, we develop and esti-mate a statistical model (a multinomial logit model)of college choice behavior. This model seeks todetermine the implicit weights (relative impor-

tances) that students place on their prior prefer-ences and other relevant variables when theymake their college choice (1,!cisions. We then in-vestigate whether important individual differ-ences exist, that is, whether same students weighthe prior preference and other celevant variablesdifferentially when choosing a college. A secondtype of individual differences is also investigated:context effects. Context effects refer to differentchoice situations, such as choosing from among achoicc set which contains one or more Ivy Leaguecolleges. A number of scenarios are constructedto illustrate the influence of several variables onthe college choices of aur students.

Some preliminary results anddescriptive statisticsWe begin the analysis of college choice behaviorby examining some relevant descriptive statisticsrelated to application set sizes, switching behav-ior, and related matters. These analyses are de-signed just to be exploratory in nature, to providethe backdrop for the statistical modeling effortsto follow.

The distributions of the application and choiceset sizes for our survey respondents are displayedin Table 4.1. Students applied to an average of3.6 colleges. However, about one-fifth of all thesestudents (21.0 percent) applied to only a singlecollege, while another one-fifth (20.2 percent) ap-plied to six or more colleges. These 1,549 stu-

27

33

Table 4.1. Applicction and choiceset sizes1

Size ofset Application set Choice set

1 21.0% 6.3%2 17.3 29.5

3 16.3 27.04 13.1 15.65 12.0 10.8

6 8.5 5.7

7 4.6 2.5

8 3.7 1.6

9 1.5 0.4

10 + 1.9 0.6

Total 100.0%2 100.0%

Mean 3.6 3.4

1. The data base for the application set sizes is the 1.549students who responded to the mail survey. The data base forthe choice set sizes is the 1.183 students who responded tothe telephone survey. Note that only students with applicationsets of greater than one were included in the second wave(the telephone survey) of this study.2. Due to rounding. the application set total does not add to100.0%.

dents submitted 5,298 admissions applications,and 63.8 percent of these admissions applicationswere accompanied by a request for financial aid.

Students who applied to more than one collegereceived an average of 3.4 admissions offers. Aconsiderable number of these high-ability highschool seniors had relatively large choice sets:37.3 percent of the students who applied to morethan one college had choice set sizes of four ormore.

As noted in Chapter 3, 21 percent of thesestudents applied to only a single college. In thesense of college choice as used in this study, thesestudents did not have a choice, since choice isdefined as selection from a set of two or morecolleges offering admission to a student. This

group represents a relatively large number of stu-dents, and some further investigation of its com-position seems appropriate.

Table 4.2 contains some descriptive statisticson a range of demographic variables for the sin-gle- and multiple-college applicant groups. Themain differences seem to lie in average SATscores, planned educational level, and parentalincome. Students in the multiple-applicant grouphave higher average SAT scores, are more likelyto plan for a graduate level of education, andcome from higher-income families. A sizable pro-portion of the single-college applicants are apply-ing to public institutions, where admission ishighly likely or guaranteed or where admissiondecisions are made on a rolling basis. It is likelythat a smaller number of these students wereaccepted to selective colleges under some formof early action.

The choice component of our multistage col-lege choice model begins with a prior preferencemeasure and then adds in other relevant varia-bles, some of which moderate this measure andsome of which represent information which be-comes completely known to students only afterthey receive their admissions offers. Our ultimatemeasure of choice was obtained during the tele-phone follow-up interview, which was conductedafter the students had made their actual collegechoice decision.

Changes between prior preferences and finalcollege choices must exist if post-admissions var-iables such as financial aid exhibit any influenceon the ultimate college choice decision. For ourstudents whose choice sets contained two or morecolleges, 60.5 percent did ultimately choose toattend the college they identified as their firstchoice. However, the 39.5 percent of studentswho switched represent a large enough group tolead us to investigate the factors which led somestudents to change their prior preferences whileothers held fast to their original college prefer-

3 4 28

Table 4.2. Comparison of single- and multiple-college applicants

Average SAT scores550-599600-649650-699700-749750-800

GenderMaleFemale

Planned educational levelGraduate schoolBachelor's/uncertain

Planned field of studySciencesEngineeringLiberal artsOther

Seif-reported parental gross income$30,000 or less$30,001-$49,999$50,000 or more

Note: Due to rounding. some totals do not add to 100.0%.

ences. Table 4.3 displays the incidence of priorpreference changes for students with varioussized choice sets.

The self-reported reasons for switching seemto relate substantially to monetary considera-tions, as the data in Table 4.4 demonstrate. About50 percent of these switchers cited cost or finan-

Single-collegeapplicants

Multipk-coPege

applicants

24.6% 17.5%20.6 19.220.6 19.220.0 21.214.2 23.0

100.0% 100.0%

57.8% 63.4%42.2 36.6

100.0% 100.0%

64.8% 79.0%35.2 21.0

100.0% 100.0%

40.2% 42.2%20.9 23.620.9 18.718.1 15.4

100.0% 100.0%

30.3% 23.7%38.3 36.631.4 39.7

100.0% 100.0%

cial aid as a prime reason for switching. Theseobservations must be tempered with the pointthat only those who switched were asked abouttheir reasons. Conceivably, those who did notswitch might have had exactly the same reasonsfor staying with their original choice.

One further exploratory inquiry involved asking

29

35

Table 4.3. Incidence of switching from original fir st-choice college

Choice set size

No. of studentschoosing theirfirst-choice .7:ollege

No. of studentschoosing anothercollege

Incidence ofswitching

2 229 111 32.6%3 185 126 40.54 120 59 33.05 51 74 59.26 39 28 41.87+ 31 30 49.2Overall 655 428 39.5%

students directly how much additional scholar-ship aid would be required to lead them to switchto their second-choice college (see Table 4.5 forthe relevant results). We asked the students fourseparate questions, related to whether $500,$1,000, $2,000, or $3,000 would lead them tochange their college choice. Even with the largestamount--$3,000--only about half the students re-ported that they would switch. These results sug-gest that it may take rather large financial in-ducements to cause students to change from their

Table 4.4. Stated reasons for notchoosing the original first-choice college'Reason Frequency

Better financial aid 27.4%Lower costs 23.1Campus visits 12.6Location 10.5Academic reputation 11.9Other 14.4

100.0%2

1. The data reported in this table refer to 271 students in thetelephone survey who reported their chosen college as differ-ent from their first-choice college (to which they were admit-ted) in the mail survey and who gave a reason for changing.2. Due to rounding, the total does not add up to 100.0%.

36

otherwise first college choices. Of course, stu-dents' answers to such direct and hypotheticalquestioning may not necessarily be valid indica-tors of actual behavior, so we need another ap-proach to assess the influence of monetary con-siderations on college choice. Such an approach,involving the construction and estimation of astatistical model of college-choice behavior, is de-scribed in the following section.

A multinomial logit modelWe now turn to documenting our multinomiallogit model of college choice behavior. In turn,we describe the formulation of the model, esti-mation issues, model specification analyses, andthe results of explorations into individual differ-ences analyses.

Model formulationThe varirbles in our choice model are describedin Table 4.6. These variables form the basemodel. We will subsequently test to see if a smallset of additional variables should be added toform an extended model.

As may be noted, there are four distinct groupsof variables, corresponding to unconstrainedprior preference measures, financial constraintsand considerations, individualinstitution inter-

Table 4.5. Stated choice intentionsif second-choice college offered anextra scholarship

Amount of extrascholarship

Percentage whosecollege choicewould change

$ 500 3.8$1,000 13.2$2,000 31.2$3,000 49.0

actions, and college-specific effects. The theoryunderlying the inclusion of these groups of vari-ables was described in Chapter 2.

To measure prior preference, three indicatorvariables are included in the model: FIRST, SEC-OND, and THIRD. These variables indicatewhether a college alternative was first, second, orthird in a student's original preference evaluationprior to receiving complete admissions and finan-cial aid information from all colleges. (If a studentwas not ultimately admitted to his or her first-choice prior preference college, then FIRST wasappropriately modified to correspond to the high-est-ranked college to which the student was ul-timately admitted. Similar adjustments weremade for SECOND and THIRD, when necessary.)We expect that FIRST, SECOND, and THIRD willall have very strong effects on choice, since theysummarize all preference-related components inour model. Naturally, FIRST should have thegreatest influence on choice, followed consecu-tively by SECOND and THIRD. With regard to thefinancial variables, incomplete data (total finan-cial aid without the grant and non-grant compo-nents; missing data on perceived renewability ofaid; occasional missing college cost data) neces-sitated the inclusion of several composite varia-bles to model out missing data effects. Grant(GRANTAID) and non-grant (OTHERAID) aid areincluded as separate variables to account for theexpected differential impact of these aid types.

Perceived renewability of aid (RENEWAL) is aninteresting heretofore uninvestigated influence oncollege choice. We expect that COSTS will havea negative influence on choice, while GRANTAIDand RENEWAL will influence a college's attrac-tiveness in a positive fashion, other factors heldconstant. The influence of OTHERAID is uncer-tain, but presumably it is not negative. Since suchaid includes loans and part-time jobs, it does notcome "free"it either has to be paid back orwork must be performed to earn it. Thus, OTH-ERAID is presumably of much less value to thestudent than GRANTAID.

By including SATFIT, we may investigate theinfluence of "academic quality zoning" on stu-dents' choices. Note that SATFIT is really definedin terms of the lack-of-fit between the college andthe student, as measured in terms of the absolutevalue of the difference between respective SATscores. It is expected that higher values ofSATFIT will have a negative influence on choice:students should prefer to be at colleges where theaverage student ability level is fairly similar totheir own (as measured by SAT scores), holdingother factors constant.

Seven college-specific indicator variables areincluded in the choice model. The top sevencollegesin terms of frequency of mentionin the original applications of our 1,549 mail sur-vey respondentsare denoted COLLEGE1,COLLEGE2, . . . , and COLLEGE7. Each of thesecolleges had at least 150 mentions across the1.549 application sets. The specific identities ofthe colleges are not crucial to our investigation;suffice it to say that they are well-known, highlyvisible, selective private institutions locatedlargely, but not exclusively, in the northeast of theUnited States. Recall that the inclusion of thesecollege-specific variables is designed to model out"brand name" effects that might not otherwise befully captured by other variables in the model(chiefly the prior preference variables). Such al-ternative-specific indicator variables are typically

31 -

37

Table 4.6. Definition of the variables included in the choice modelVariable Definition

Uncon.strained prior preferenceF IRST An indicator variable denoting

preference ra Acing (in March):erence college, and equals 0 ot

SECOND An indicator variable denotingpreference ranking (in March):preference college, and equals

THIRD An indicator variable denotingpreference ranking (in March):erence college, and equals 0 ot

Financial constraints and considerationsCOSTS

COSTSM

TOTALAID

CRANTAID

OTHERAID

RENEWAL

RENEWM

IndividualinstitutionSATF1T

SATM

College-specific effectsCOLLEGE1

COLLEGE2 throughCOLLEGE7

whether a college was the first-choice in the originalequals 1 if this college was the first-choice prior pref-herwise.whether a college was the second-choice in the originalequals 1 if this college was the second-choice prior0 otherwise.whether a college was the third-choice in the originalequals 1 if this college was the third-course prior pref-herwise.

Total costs (in $000s) to attend a college: includes tuition, room and board charges,and other e:-penses. If costs are missing, then COSTS = 0.An indicator variable for missing total costs: equals 1 if COSTS are missing (COSTS= 0). and equals 0 otherwise.

Total financial aid (in $000s), if only a total aid figure was reported and individual aidbreakdowns into grant and non-grant aid were not available; equals 0 otherwise.Grant aid (in S000s) if separate grant and non-grant breakdowns were reported: equals0 otherwise.Other aid (in $000s)non-grant aid (loans and part-time work)if separate grant andnon-grant breakdowns were reported; equals 0 otherwise.Self-reported perceived renewal possibility for financial aid: coded as 1 = "None,"2 = "Possible," 3 = "Probable," and 4 = "Certain" if renewal possibility was re-ported, and equals 0 otherwise. (If no aid was awarded, then RENEWAL is set equalto 0.)An indicator variable for missing values of RENEWAL: equals 1 if RENEWAL ismissing, unknown, or unreported (RENEWAL = 0), and equals 0 otherwise. If astudent receives no aid, then RENEWM is set equal to 1.

interactionsThe SAT "fit" between a college and a student: equals the absolute value of thedifference between the student's SAT score and the average SAT score of all studentsat a college if both SATs are available, and equals 0 otherwise.An indicator variable which equals 1 if a college's mean SAT scores were not avail-able, and equals 0 otherwise.

An indicator variable that equals 1 for the most frequently mentioned college interms of applications submitted by our 1,549 mail survey respondents, and equals 0otherwise.Indicator variables for the second through seventh most frequently mentioned collegesin terms o4' applications submitted by our 1,549 mail survey respondents.

38 32

included in choice models such as the one beingconstructed here (c.f. Ben-Akiva and Lerman1985).

Descriptive statistics for each of the variable.in Table 4.6 are displayed in Table 4.7. "i hesestatistics are for the 3,882 college alternatives inthe 1,101 choice sets that were available for anal-ysis. Seven of the 1.108 students with choice-setsizes of at least two included tied first-choicecolleges. These were not used in the analysis.

The following are observations about the sum-mary statistics reported in Table 4.7:

Some of the 1,101 choice sets had ties reportedfor the second-choice college. This accounts forthe mean value of SECOND exceeding that ofFIRST.

The mean total costs of attendance at the col-leges to which these 1,101 students were admit-ted was $10,494, ignoring the 35 college alterna-tives out of a total of 3,882 (0.9 percent) for whichcollege cost data were missing. Thus, these stu-dents are obviously opting in substantial numbersto apply to the selective, well-known, expensiveprivate ccileges.

With regard to perceived renewability, 64.2 per-cent of the 3,882 college alternatives to which our1,101 students were admitted had missing data.Only 3.1 percent of these were aid awards wherethe students did not report a value for perceivedrenewability; the other 61.1 percent correspondto non-aid award situations, where perceived re-newability is irrelevant (and where, by definition,RENEWAL = 0).

The average difference between college and stu-dent SAT scores. averaged over all the choicealternatives to which the students were admitted,was 91.7.

By summing the mean values for COLLEGEI,. . . , COLLEGE7, it may be noted that only about16.4 percent of these college alternatives werethe seven most frequently mentioned colleges.That is, about one-sixth of the 3,882 admissions

Table 4.7. Descriptive statistics forvariables in the choice model

Summary statistics

MeanStandarddeviation

FIRST 0.213 0.4i0SECOND 0.223 0.410THIRD 0.181 0.385COSTS 10.494 4.248COSTSM 0.009 0.095TOTALAID 0.065 0.666GRANTAID 1.239 2.344OTHERAID 0.503 1.197RENEWAL 1.003 1.408RENEWM 0.642 0.479SATFIT 91.706 62.999SATM 0.072 0.259

COLLEGE) 0.025 0.156COLLEGE2 0.024 0.154COLLEGE3 0.023 0.151COLLEGE4 0.025 0.156COLLEGE5 0.024 0.152COLLEGE6 0.016 0.125COLLEGE7 0.027 0.161

Note: These descriptive statistics are based on all choice setalternatives for the 1.101 choice sets which were used todevelop the multinomial logit model of college choice behav-ior.

offers to these 1,101 students were from the topseven colleges.

Preliminary analysisA useful preliminary analysis of our choice datais reported in Table 4.8. Means for selected var-iables from Table 4.6 are shown for first-choicecolleges (the colleges actually chosen), second-choice colleges, third-choice colleges, and othercolleges. Some interesting and apparently pre-dictable patterns seem to emerge.

33

39

Table 4.8. Means of selected choice model variables, by final choice position'

Overall2

First-choice(chosen)collegealternatives

Second-choicecollegealternatives

Third-choicecollegealternatives

Othercollegealternatives

COSTS 10.494 10.794 10.551 10.378 10.164GRANTAID 1.239 1.863 1.056 0.969 0.936OTHERAID 0.503 0.745 0.451 0.422 0.341RENEWAL 1.003 1.310 0.959 0.822 0.837SATFIT 91.706 77.394 87.352 95.417 110.880COLLEGE! 0.025 0.052 0.022 0.013 0.006COLLEGE2 0.024 0.035 0.021 0.024 0.016COLLEGE3 0.023 0.043 0.025 0.011 0.008COLLEGE4 0.025 0.051 0.023 0.008 0.011COLLEGES 0.024 0.031 0.028 0.023 0.011COLLEGE6 0.016 0.015 0.022 0.013 0.012COLLEGE7 0.027 0.027 0.033 0.031 0.016

1. In this table, "choice position" refers to the actual final ranking of alternative colleges to which students wereadmitted. Thus. "first-choice Ichasenr refers to the college actually chosen by the student: "second-choice-refers to the college the student reported he or she would attend if not attending the first-choice college.2. Means listed under the "Overall" column are taken directly from Table 4.7. They are reported here fiff com-parative purposes and to assist in the interpretation of the other means reported in this table.

COSTS aecrease slightly as we move from first-choice to other high-choice colleges. For exam-ple, the average first-choice college has totalcosts of $10,794, while the average third-choicecollege has total costs of $10,378. This small de-crease is noteworthy: It appears that the high-cost private and the low-cost public college op-tions are sprinkled throughout these students'choice sets, rather than concentrated at the topor bottom. This would also suggest that costs arenot too crucial a factor at the level of collegechoice.

Note that COSTS and other variables in Table4.8 are being examined one at a time, rather thansimultaneously. Viewed in this fashion, highercosts appear to be slightly positively associatedwith choice, presumably because many collegesperceived by students to be desirable on other

grounds are also costly. We expect that when theeffect of costs is estimated simultaneously withother variables that costs will turn out to be neg-atively associated with choice.

The mean GRANTAID and OTHERAID decreaseas we move from first-choice to other high-choicecolleges. For example, the mean GRANTAID of-fered by first-choice colleges was $1,863, whilethat offered by third-choice colleges was only$969-a reduction of about $900. Since COSTSonly decrease by a small amount (about $400 be-tween first- and third-choice colleges), collegecosts do not account for the differences in aver-age grant amounts from first- to third-choice col-leges. These data suggest that GRANTAID (and,perhaps to a lesser extent, OTHERAID) has aninfluence on choice behavior.

RENEWAL drops sharply as we move from first-

4 0 34

choice (mean RENEWAL value of 1.310) to third-choice (0.822) college alternatives. This is consis-tent with students paying considerable attentionto perceived renewability of financial aid awardswhen they make their college-choice decisions.This evidence is consistent with the view that asperceived renewability decreases, so does thechoice probability associated with a. particularcollege alternative.

SATFIT increases considerably from first-choice (mean SATFIT value of 77.394) to third-choice (95.417) college alternatives. This is con-sistent with students preferring to attend collegeswhere the average SAT score of the other studentsis similar to their own.

As noted earlier, about 16.4 percent of the3,882 college alternatives confronting our 1,101students were from the top seven colleges (interms of frequency of mention). This concentra-tion increases to 25.4 percent when we look onlyat first-choice college alternatives. Not surpris-ingly, the colleges attracting the largest numberof applications are also chosen by students withhigh frequency.

In summary, this preliminary analysis suggeststhat GRANTAID, RENEWAL, and the college-spe-cific indicator variables have positive influenceson choice probabilities. Lack of SAT fit (as mea-sured by the variable SATFIT) appears to have anegative influence on choice probabilities.

Model estimationA multinomial logit model was estimated usingthe variables described in Table 4.6. A linearadditive functional relationship was assumed.The results of this estimation are displayed inTable 4.9.

The results reported in Table 4.9 are for anexplosion depth of one. That is, only the first-choice rank-ordered choice sets were used in theestimation. Attempts to use the second- andthird-ranked colleges to form Aditional choicesets, as described in Chapman and Staelin 1982,

were unsuccessful. In testing whether the sec-ond-choice ranking could be used, the conclusionwas that explosion to a depth of two was notappropriate. (Thus, higher-order explosions werenot investigated.) The relevant chi-squared teststatistic value was 84.8 (with the correspondingcritical chi-squared value of 36.2, for 19 degreesof freedom and a 1 percent level of significance).Thus, we reject the null hypothesis that the firstand second explosion depths yield equivalent rel-ative-importance weights. Apparently these stu-dents use a different weighting system from thatused for the actual college chosen for evaluatingsecond- and possibly subsequent-choice alterna-tives in their rank ordering.

The log-likelihood ratio index (LLRI) value of0.419 is exceptionally high for such college-choicestudies. As noted in Appendix 1, values of LLRIin the 0.10-0.35 range are typical in collegechoice studies employing the multinomial logitmodel. This LLRI value appears to exceed thoseachieved in other published studies of collegechoice behavior (where noncollege alternativesare not considered.) This high level of statisticalperformance presumably follows from our effortsto carefully collect the relevant data at the keypoints in the college choice process. The rela-tively homogeneous nature of our samplecon-sisting of high-ability studentsmay also havecontributed to this result, since these studentsmay have been more consistent in their choicebehavior than would a more heterogeneous sam-ple.

Several other measures of the goodness-of-fit(statistical performance) of our model were de-veloped. We may use the statistical model to pre-dict our students' actual college choices and thencompare such predictions to actual college en-rollment levels for our sample. In such an anal-ysis, the unit of investigation becomes the col-lege, rather than the student.

The correlation between predicted and actualcollege enrollments, when aggregated across all

35 41

Table 4.9. Results of estimating the choice model

VariableCoefficientestimate

Standarderror T-Ratio

FIRST 3.2762 0.1693 19.346SECOND 1.9061 0.1589 11.992THIRD 1.3063 0.1616 8.085

COSTS 0.1:313 0.0195 6.716COSTSM 0.0400 0.5105 -0.078TOTA LAID 0.0770 0.1113 0.692GRANTAID 0.2907 0.0360 8.068OTHERAID 0.0158 0.0550 0.029RENEWAL 0.3062 0.1344 2.279RE NEWM 0.6075 0.3909 1.554

SATFIT 0.0041 0.0015 -2.754SATM 0.0631 0.2548 0.24,8

COLLEGE! 2.0964 0.3314 6.326COLLEGE2 1.2433 0.3323 3.742COLLEGE3 1.7104 0.3351 5.105COLLEGE4 1.5709 0.3222 4.875COLLEGES 0.6886 0.3336 2.064COL LEGE6 0.8403 0.4214 1.994COLLEGE7 0.0676 0.3123 -0.216

Summary statisticsNumber of choice setsInitial log-likelihood = -1289.6Final log-likelihood = -749.0Log-likelihood ratio index = 0.419

Note: Refer to the discussion in Appendix 1 for details and interpretations of the various log-likelihood statistics.

1,101 students, was 0.856. The average percent-age absolute error in prediction across the 24colleges with at least ten actual enrollments fromour sample of students was 11.1 percent. ("Per-centage absolute error" for a single college equals100.0 times "absolute error" divided by the actualenrollment value. Absolute error equals the ab-solute value of the predicted enrollment minusthe actual enrollment.) For the 60 colleges withat least five actual enrollments, the correspondingaverage percentage absolute error was 16.2 per-

cent. Thus, in aggregate, we are able to predictcollege choices of these high-ability students witha high degree of precision.

Model-specification analysisIn addition to the variables described in Table4.6, some other variables were of interest as po-tential determinants of college choice behavior.Because our prior feelings about these variableswere less strong than those about the variablesin Table 4.6, we have reserved these variables

4 2 36

for specific statistical testing to determine if theyshould be added to the base model. Our generalphilosophy is to seek a parsimonious (simple)model form, unless strong evidence exists to sup-port the embracing of a more complicated modelform (with, for example, more variables).

The additional variables are described in Table4.10. FATHER and MOTHER measure the poten-tial of legacy effects to influence choice. DIS-TANCE proxies the costs (monetary and psycho-logical) associated with travel to a distant college.APPNOAID represents the possible negative ef-fect of a college denying financial aid to an aidapplicant. PFIRST, PSECOND, and PTHIRD areinteractive variables between portable (personal)scholarship aidsuch as National Merit Schol-arships that are awarded to the student for useat whatever college he or she choosesand priorpreference. Inclusion of these variables in themodel was designed to check on a hypothesis thatstudents with relatively large amounts of portableaid would be more likely than others to act con-sistently with their prior preferences, since mon-etary considerations would be less constraining.Of course, such students might have applied to

different colleges in the first instance. Finally, toassess the possibility of financial aid exerting anonlinear influence on college choice (rather thanthe linear effect postulated by the base model),quadratic terms for the two key aid variables--GRANTAID and OTHERAIDwere aided to themodel.

The results of the statistical tests for the sev-eral groups of variables are reported in Table4.11. In all cases, the extra variables did not addsignificantly, given that the base-model variables(described in Table 4.6) were already included inthe multinomial logit model of college choice be-havior. Thus, we conclude that none of these var-iables should be added to the base model.

It is interesting to note that parental legacyeffects, portable scholarship aid, distance, andthe effect of applying for but being denied aid ata college apparently are not relevant factors atthe level of college choice. The parental legacyand distance effects may, of course, have beeninfluential at the search stage in leading to thecolleges to which students applied in the firstinstance. However, at the choice stage, they ap-pear to have no residual influence.

Table 4.10. Other variables tested in the extended choice modelVariable Definition

FATHER

MOTHER

DISTANCE

APPNOAID

PFIRSTPSECONDPTHIRDGRANT2OTHER2

An indicator variable that equals 1 if a student's father attended a college, andequals 0 otherwise.An indicator variable that equals 1 if a student's mother attended a college, andequals 0 otherwise.The distance (in 000s of miles) from the campus of a college to the residence of astudent.An indicator variable that equals 1 if a student applied for and was denied aid at acollege, and equals 0 otherwise.Amount of portable (personal) scholarship aid (in $000s) times FIRST.Amount of portable (personal) scholarship aid (in $000s) times SECOND.Amount of portable (personal) scholarship aid (in $000s) times THIRD.Equals GRANTAID*GRANTAID.Equals OTHERAID*OTHERAID.

37 4 3

Table 4.11. Results of statistical tests on the extended choice model form'

Group of variables testedCalculatedtest statistic

Degreesof freedom

Criticalvalue Conclusion=

FATHER. MOTHER 2.6 2 9.2 n/sDISTANCE 3.2 1 6.6 n/sAPPNOAIL 0.2 1 6.6 n/sPFIRST, PSECOND, PTHIRD 5.4 3 11.3 n/sGRANT2. OTHER2 0.4 2 9.2 n/s

1. A 1 percent level of statistical significance was used in these tests.2. Under "Conclusion." "n/s" means that the calculated test-statistic value does not exceed the critical value. sothe null hypothesis (that the indicated group of variables has no influence on college choice) cannot be rejected.Thus, such variables should not be added to the model, since the most parsimonious representation corresponds tothe model without such variables.

Interpretation ofthe choice model results

Based on the choice model results reported inTable 4.9, the main determinant of college choiceappears to be prior preference. Financial consid-erations are relevant, but they are clearly sec-ondary. Also, perceived renewability of aidawards and SATFIT are statistically significant inthe predicted directions. The college-specific ef-fects appear to be quite substantial, as well. Insummary, these students appear to take manythings into account when choosing colbges.

A number of quantitative comparisons may bemade using the coefficient estimates to illustrateand interpret the results. Given that the focus ofthis study is on no-need scholarship aid, it willbe useful to interpret these results in terms ofimplicit equivalent amounts of scholarship aid.

Since our multinomial logit model is essentiallya utility or value model, it will be convenient tointerpret a coefficient estimate times the value ofthe corresponding variable as representing (par-tial) utility points. For example, based on theresults reported in Table 4.9, a typical studentderives 3.2762 utility points from a first-choiceprior-preference college. Such a student derives

(0.2907) (5.000) = 1.4535 utility points from a$5,000 scholarship aid offer. A college with costsof $10,000 would be interpreted as yielding(-0.1313) (10.000) = 1.313 utility points for atypical student. Here, the negative sign on theCOSTS coefficient signifies that higher-cost col-leges are, holding other things constant, less pre-ferred (i.e., students receive less utility or valuefrom higher-cost colleges, ceteris paribus).

The difference between a first- and second-choice prior preference college is 1.3701 utilitypoints (3.2762 1.9061). Since each $1,000 ofscholarship aid is implicitly evaluated as beingequivalent to 0.2907 utility points, a second-choice college that offers an extra $4,713 schol-arship would just offset the difference betweenbeing the second choice and being the first choiceon a prior preference basis. For a third-choiceprior preference college that wishes to competewith a first-choice college, an extra scholarshipof 1,000*(3.2762 1.3063)10.2907 = $6,776would be required to bring it up to par with thefirst-choice college. This illustrates that moneywill "buy" students, but it seems that the costassociated with this is quite substantial.

With regard to the financial variables, each$1,000 of total costs penalizts a college 0.1313

4 4

utility points, while each $1,000 of scholarshipaid adds 0.2907 utility points to the overall utilityor value of a college. This suggests that about $2of extra costs may be approximately offset by $1of scholarship aid. However, we are operating atthe choice stage here: Too expensive collegesfrom the perspective of the student or the stu-dent's parentsmight have been ruled out of con-sideration at an earlier stage, prior to submittingapplications to colleges.

Non-grant aid (OTHERAID) appears to have nodetectable influence on choice behavior. It nei-ther adds to nor subtracts from the overall desir-ability of a college.

Perceived renewability is weighed positively bystudents when they evaluate colleges. Each extrapoint of perceived renewability yields an addi-tional 0.3062 utility points for a school. Also, therelative values of the coefficients on RENEWALand RENEWM suggest that these students implic-itly evaluate no information about renewability asbeing approximately equal to a value of 2 (0.6075/0.3062) on our four-point renewability scale(where "2" = "Possible"). A $5,000 scholarshipwith no chance of being renewed yields a totalutility of (5.000) (0.2907) + (1) (0.3062) = 1.7597,taking only the scholarship and renewability intoaccount. An $1,840 scholarship with guaranteedrenewability would yield approximately the sameamount of utility. Thus, it seems that studentsimplicitly discount nonrenewable scholarship aidto a substantial extent. These results suggest thatcolleges should ex:end a considerable amount ofeffort in specifying renewability conditions in theclearest possible terms. If a student is in doubt,he or she may implicitly downgrade a college'sfinancial aid offer, especially compared to aid of-fers which the student perceives to ha' highchances or to be guaranteed of being reneN, ed.

With regard to SATFIT, each 100 points of SATdifference (between the student's SAT score andthe average SAT score of all students at a college)reduces the value of a college by 0.41 utility

points. This is approximately equivalent to thevalue of a scholarship of $1,410.

The college-specific effects are substantial,ranging from about 0 to 2.1 utility points. Theaverage college-specific effect (for the top sevencolleges in terms of frequency of mention) isequal to 1.155 points. TI-is is approximately equalto the value of a scholarship of $3,972. Thus, ina choice set with just two colleges, a non-"topseven" college would have to offer a scholarshipof $3,972 to be approximately equivalent in utilityterms to an average top seven college (assumingthat all other things were equal).

The missing data correction factorsCOSTSM,TOTALAID, and RENEWMare, in general, notstatistically significant. Thus, they have no im-pact on the model's results; however, they doserve to account for these missing data effects.

These and other related examples will be de-scribed later in this chapter, when we investigatemore fully the implications of these findings aboutthe determinants of college choice.

Individual differences analysesThe relative-importance weights results reportedin Table 4.9 are for au students. To assesswhether students' backgrounds influence theirchoice weights, and to assess whether theseweights are stable across different choice sit-uations, individual differences analyses may beconducted. These analyses require the use of sta-tistical-pooling testsfor example, are the rela-tive-importance weights of men identical (in astatistical sense) to those of women? The frame-work of these pooling tests for the multinomiellogit model is described in Appendix 1.

Demographic variables. We tested for hetero-geneity of weights for the following demographicvariables (and subgroups of students): SAT scores("average SAT score less than or equal to 675";"average SAT score more than 675"), genrl,q-("male"; "female"), planned educational .

39 45

Table 4.12. Individual differences analysis: Pooling test results fordemographic variables'

Calculatedtest statistic

Degreesof freedom

Criticalvalue Conclusion

Average SAT scores 24.2 19 36.2 n/s2(2 groups)

Gender 19.6 19 36.2 n/s(2 groups)

Planned educational level 10.8 19 36.2 rds(2 groups)

Planned major field ofstudy

94.8 38 61.1 n/s

(3 groups)Parental income

(3 groups)65.8 38 61.1 Signifi-

cant

1. A 1 percent level of statistical significance was used in these tests.2. Under "Conclusion," "n/s- means that the calculated test-statistic value does not exceed the critical value. sothe null hypothesis that the groups have identical relative-importance weights cannot be rejected; "significant"means that the groups apparently are characterized by different relative-importance weights.

("bachel.)r's or uncertain"; "graduate school"),planned major field of study ("sciences"; "engi-neering"; "other"), and parental income level("$30,000 or less"; "$30,001$49,999"; "$50,000or more"). The results of these tests are displayedin Table 4.12.

The pooling test results shown in Table 4.12indicate that only in the case of parental incomelevel are the relative-importance weights differ-ent. Thus, we may conclude that the weightsreported in Table 4.9 adequately describe all SATlevels (in the range represented in our sample,550-800), men and women, all planned majorfields of study, and all planned educational levels(bachelor's only versus graduate school inten-tions). There are no apparent individual differ-ences based on these demographic variables.However, since significant differences existacross parental income groups, a detailed exam-ination of these differences in appropriate.

Parental income effects. The coefficients forthe various parental income groups are shown in

4 6

Table 4.13. Also, for reference purposes, meansof selected choice model variables for the groupsare displayed in Table 4.14. Major differencesacross the parental income groups are describedbelow.

The impact of GRANTAID is great on low-in-come students (0.4448 utility points per $1,000 ofscholarship), less for medium-income students(0.2236 per $1,000), and then great again for high-income students (0.4064 per $1,000). OTHERAIDappears to be irrelevant for all groups. The low-and medium-income coefficients on GRANTAIDfollow a predictable pattern: As income in-creases, there is less sensitivity to financial con-siderations. However, the influence of GRANTAIDis almost as great for the high-income as it is forthe low-income group.

The rise in the GRANTAID effect as we movefrom the medium- to the high-income group may,in the first instance, appear odd. The data inTable 4.14 indicate that the average GRANTAIDof $548 for high-income students is considerably

Table 4.13. Coefficient estimates for different parental income levels

Variable

All studentswith reportedparentalincome

Income groups

Lowincome(less than$30.01,0)

Mediumincome($30.001 to$49.999)

Highincome450.000or more)

FIRST 3.4108** 3.2068** 3.4437** 3.7543**SECOND 2.0608** 1.7946** 2.1517** 2.1749**THIRD L4487** L5682** 1.4897** 1.3350**COSTS -0.1439** -0.1962** -0.1815** -0.1260**COSTSM -0.1803 -1.9300 1.0438 1.2213TOTALAID 0.1032 0.2276 0.2027 -1.0860GRANTAID 0.2964** 0.4448** 0.2236** 0.4064**OTHERAID -0.0131 0.0525 0.0222 -0.1494RENEWAL 0.4340** 0.7650* 0.4506** 0.1597RENEWM 1.0189* 2.3328* 0.5931 0.6266SATFIT -0.0044** 0.0002 -0.0024 -0.0118**SATM -0.0206 0.5215 -0.0247 -0.5516COLLEGE! L9919** 2.6034** 1.8458** 1.9592**COLLEGE2 1.3756** 1.6991 1.4773* 1.2436*COLLEGE3 1.7753** 0.8033 2.0738** 1.8866**COLLEGE4 1.6666** 3.1201** 1.6991** 1.3267*COLLEGES 0.6535 0.4572 1.0031 -0.0451COLLEGE6 1.0268* 0.6286 2.5554** 0.1730COLLEGE7 0.0171 0.0978 -0.1141 0.1120

Summary StatisticsNo. of choice sets 976 228 359 389Initial LL -1138.2 -255.4 -420.0 -462.8Final LL -652.1 -145.1 -245.7 -228.4LLRI 0.427 0.432 0.415 0.506

Note: Refer to the discussion in Appendix 1 for details and interpretations of the various log-likelihood statistics.Significance at the 1 percent 15 percent] level is denoted by "**" ["*"] (one-tailed test).

smaller than the corresponding figure for low-income students ($2,228). Thus, the high-incomestudents must be responding to the psychologicalimpact of receiving scholarships: it's not just themoney, it's the recognition that goes along withreceiving such scholarship aid. Further supportfor this recognition-effect interpretation may befound by looking at the relationships among other

coefficients across income groups. High-incomestudents are much less sensitive to COSTS thanare low-income students, so monetary consider-ations are not that important in and of them-selves. Also, high-income students do not partic-ularly value renewability of aid, at least not to theextent that low-income students do.

There are important differences in terms of the

41 4 7

Table 4.14. Means of selected choice model variables, by income groups

Variable

All studentswith reportedparentalincome

Income groups

Lowincome(less than$.30.000)

Mediumincome($30.001 to$49.999)

Highincome($50.000or more)

COSTS 10.449 9.842 10.062 11.140GRANTAID 1.275 2.228 1.493 0.548OTHERAID 0.512 0.900 0.635 0.184RENEWAL 1.008 1.495 1.219 0.544

SATFIT 90.965 85.238 95.085 90.371

COLLEGE! 0.025 0.017 0.021 0.032COLLEGE2 0.025 0.014 0.018 0.036COLLEGE3 0.023 0.014 0.018 0.032COLLEGE4 0.025 0.018 0.018 0.034COLLEGES 0.021 0.013 0.022 0.025COLLEGE6 0.015 0.009 0.011 0.022COLLEGE7 0.026 0.023 0.029 0.025

impact of COSTS as we move across the incomegroups. Each $1,000 of cost represents a reduc-tion of 0.1962 utility points for a low-income stu-dent, while the corresponding figures for me-dium- and high-income students are 0.1815 and0.1260, respectively. This drop in importance inCOSTS as income increases is consistent with theexpected relationship between financial statusand sensitivity to financial considerations. How-ever, note that even for the high-income students,COSTS are a significant factor in the collegechoice decision.

The influence of perceived renewability isgreatest for low-income students (01650 utilitypoints per perceived renewability-srale point),next highest for medium-income students (0.4506utility points per perceived renewability-scalepoint), and apparently irrelevant for high-incomestudents. Once again, this pattern is consistentwith lower-income students having the greatestsensitivity to financial considerations.

The influence of SATFIT on choice is statisti-

cally significant only for high-income students:Each point in SAT difference represents a de-crease of 0.0118 utility points. Thus, a 100-pointSAT difference would correspond to a decreaseof 1.18 utility points. The model predicts thatsuch a 100-point difference for a high-income stu-dent could be overcome with a scholarship ofapproximately 82,904.

As income increases, so does the concentrationof colleges in the top seven. The data in Table4.14 indicate that about 10.8 percent of the low-income students' college alternatives are concen-trated in the top seven, while the correspondingfigures for medium- and high-income students are13.7 percent and 20.6 percent, respectively.(These percentages are the sums of the means ofthe indicator variables for thE, top seven colleges.)However, the coefficient estimdres for the variousincome gimps reported in Tab3e 4.13 suggest thatthe overall amportance of the top seven college-specific effectti does not change systematicallyacross the v,irious income f.,,,roups. The mean col-

42

Table 4.15. Choice context effect groups

Group definitionNumber ofchoice sets

"Ivy League" effect'Group 1: IVY-0Group 2: IVY-1

Group 3: IVY-2 +

"COFHE" effect2Group 1: COFHE-0Group 2: COFHE-1

Group 3: COFHE-2 +

All choice .lets containing zero Ivy League colleges.All c'aoice sets containing one Ivy League college.All choice sets containing two or more Ivy League colleges.

All choice sets containing zero COFHE colleges.All choice sets containing one COFHE college.All choice sets cGntaining two or more COFHE colleges.

665

226

210

1.101

488

256

357

1 101

I. The "Ivy League" schools were defined to include the traditional Ivy League institutions (Brown. Columbia.Cornell, Dartmouth, Harvard, University of Pennsylvania. Princeton. and Yale). plus MIT and Stanford.2. The "COFHE" colleges and universities consist of the 30 institutions that are members of the Consortium onFinancing Higher Education. The members of COFHE include Amherst. Barnard, Brown, Bryn Mawr, Carleton,Chicago, Columbia, Cornell. Dartmouth, Duke, Harvard and Radcliffe Colleges. Johns Hopkins. MIT. MountHolyoke. Northwestern, University of Pennsylvania, Pomona, Princeton, Rochester. Smith, Stanford. Swarthmore,Trinity. Vanderbilt, Washington University. Wellesley, Wesleyan University, Williams, and Yale.

lege-specific effect for the top seven colleges is1.3442 for low-income students, with the corre-sponding figures for medium- and high-incomestudents being 1.5058 and 0.9509, respectively.

Thus, in summary, there appear to be predict-able patterns of change in relative-importanceweights as income increases: sensitivity to finan-cial considerations generally decreases as incomeincreases.

Context effects. In assessing the possibility ofindividual differences based on choice-context ef-fects, we are interested in exploring variation inrelative-importance weights for students who facedifferent types of choices. The question of inter-est is: Do students who face certain kinds ofchoices and choice sets weigh things differentlythan other students?

To test for context effects, we split our 1,101choice sets into a number of non-overlapping sub-groups. The specific context effects that we chose

to investigate are displayed in Table 4.15. The"L'y League" and "COFHE" effects address thepossibility that students who are considering well-known, nationally prominent, private (expensive),and selective college alternatives may differ fromstudents who do not face such choices. Further-more, as the concentration of these kinds ofschools in a choice set changes, so might therelative-importance weights on the determiningfactors.

The Ivy League schools are, of course, wellknown. The COFHE schools were chosen as aseparate category to denote a larger group of na-tionally prominent private colleges and universi-ties. See the notes to Table 4.15 for precise def-initions of which institutions were included inthese groups.

The relevant pooling test results are reportedin Table 4.16. In each case, the null hypothesisis that the coefficients are equal for each of the

471 : 4 9

Table 4.16. Results of the context-effects individual-differences analysis'Calculated Degreestest of Critical

Context effect analyzed statistic freedom value ConelliSion

"Ivy League'' effect 30.6 31 52.2 n/s2

"COME" effect 30.0 31 52.2 n/s

1. A 1 percent level of statistical significance was used in these tests.2. Under "Conclusion:* 'Ws means that the calculated test-statistic value does not exceed the critical value. sothe null hypothesis that the groups have identical relative-importance weights cannot be rejected.

groups. The rejection of this null hypothesiswould be consistent with the presence of contexteffects; that is, relative-importance weights dodiffer by choice situation.

The results reported in Table 4.16 indicate thatIvy League and COFHE context effects are notpresent here. Apparently, our high-ability stu-dents use about the same relative-importanceweights in choosing colleges regardless of the de-gree of concentration (composition) of theirchoice sets with Ivy League and COFHE institu-tions.

Further context-effects testing (e.g., for stu-dents primarily choosing among small colleges)was not possible due to limitations of availabledata. Finer breakdowns of choice sets than theexamples tested here would have yielded groupsof data with insufficient numbers of choice setsto permit the estimation of a multinomial logitmodel in each subgroup. With a model of our size(19 variables), a minimum of several hundredchoice sets are needed to permit estimation withsuitable levels of statistical precision (Chapmanand Staelin 1982).

Concluding remarks regarding individual dif-ferences. The general robustness of our relative-importance weights is especially notable. Of thevarious individual difference possibilities exam-ined, only differences in the relative-importance

weights related to income were detected. Noother individual difference or context effects areapparently in evidence here.

In essence, these results suggest that high-abil-ity studentsregardless of demographic back-ground (except for income) or choice context/set-tingare consistent in their implicit views as tothe relative weights of the various factors evalu-ated during the college choice decision-makingprocess. Thus, our relative-importance weightsin Table 4.9 appear to be widely applicable tohigh-ability students of the type studied here andin the range of college choice contexts typicallypresent for such students.

Interpreting the choice modelresultsTo provide further interpretation of the choicemodel results, we now turn to constructing anumber of examples (cases, scenarios, illustra-tions) to apply these results. Our primary interesthere is in examining how choice probabilities aredetermined in various circumstances, and espe-cially how financial aid influences such choiceprobabilities.

The various choice-probability calculationswhich follow all use the multinomial logit modeldescribed in Chapter 2 (and Appendix 1), as it

50 44

was operationalized and estimated in this chapter,as well as the coefficient estimates reported inTable 4.9 and, for individual differences, in Table4.13. As will become apparent, these probabili-ties depend on the choice situationwhat col-leges are available and where the colleges standin terms of the multinomial logit model's variables(described earlier, and listed in Table 4.6).

To illustrate the method of calculating the var-ious choice probabilities under various scenarios,Appendix 4 contains a detailed numerical exam-ple. The illustrative examples used in the re-mainder of the chapter will, in general, be con-siderably less complicated than the exampledescribed in Appendix 4.

Preliminary definitions and discussionIn the various examples that follow, the term "ef-fective cost of scholarship aid" (or some variant)is used frequently. It is important to clarify anddefine this term precisely, since it is of greatimportance in interpreting the choice model re-sults.

As is discussed in these examples, we find thata $1,000 scholarship is estimated to move an in-different student (one who is equally inclined to-ward each of two colleges) from 50-50 choiceprobabilities to 57.2-42.8 percent choice proba-bilities, in favor of the college awarding the extra$1,000 scholarship. What is the actual and effec-tive cost of a college awarding such a student a$1,000 scholarship?

The actual cost of such a scholarship is, ofcourse, $1,000 to a student who ultimatelychooses to enroll at the college. However, thisdoes not take in account several considerations,chiefly the likelihood of the student enrolling evenin the absence of a scholarship.

To move toward a determination of the "effec-tive cost of scholarship aid," we may begin bynoting that the initial expected enrollment prob-ability for the "indifferent" student described

above is 50.0 percent. A $1,000 scholarship in-creases the expected enrollment probability from50.0 percent to 57.2 percent. For a student whoactually chooses to enroll, the scholarship cost is$1,000 to the college. However, not all studentsactually enroll. Furthermore, some of such schol-arships (actually 50 percent in this case) will inev-itably go to students who ultimately would havechosen to enroll at the college even in the absenceof the $1,000 scholarship.

The "effective cost of scholarship aid" may bedefined as the expected cost of scholarship aid(which equals the amount of the scholarship aidmultiplied by the enrollment probability in thepresence of the aid) divided by the change inenrollment probability induced by the scholarshipaid. Thus, in our example, the effective cost ofscholarship aid is (1000) (0.572)/(0.572 0.500)= $7,944. Thus, effective cost per additional stu-dent is considerably above actual cost.

Another way to arrive at this result is to con-sider a group of 100 such students. With no aid,50 would be expected to enroll. With $1,000 aidoffered to all 100 students, the cost of such ascholarship program would be $57,200, corre-sponding to the $1,000 scholarships claimed byeach of the 57.2 students who enroll. Thus, theextra 7.2 students "cost" $57,200 in scholarshipaid, or $7,944 per extra student.

The intuition behind this effective cost of schol-arship aid figure is as follows. Much of the aid isawarded to students who would have chosen toenroll at the college even in the absence of theaid. Furthermore, the use of the $1,000 of schol-arship aid only marginally improves the college'schance of being chosen (from 50 percent to 57.2percent).

Several other considerations about this defini-tion of "effective cost of scholarship aid" shouldbe noted. First, this is defined on a per-year basis.The implicit multi-year nature of financial aidawards at most collegesstudents in good aca-

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demic standing being eligible for "like" aid insubsequent yearsmeans that the effective costof scholarship aid should probably be multipliedby four, to reflect the overall financial commit-ment from the college's viewpoint. Second, theeffective cost of scholarship aid does not taketuition income into account. The tuition incomegenerated by a student enrolling at a college of-fering such aid would serve to partially offset thecost of the aid to the college.

Example 1: Prior preferences andchoice probabilitiesWe begin by assessing the influence of prior pref-erences on choice probabilities. Suppose the fol-lowing situation exists:

Choice setcompositionPrior preferencesituation

Financialconsiderations

College-specificconsiderations

Other relevantfactors

Two colleges, denoted as collegesA and B.College A is the first-choice priorpreference college alternative;college B is the second-choiceprior preference alternative.Colleges A and B are equal onCOSTS, GRANTAID, andOTHERAID.Colleges A and B are not topseven colleges (or, equivalently, itmay be assumed that they areboth average top seven colleges).Colleges A and B are equal onRENEWAL and SATFIT.

In this situation, our statistical model would pre-dict that the student would choose the highest-preference college with a probability of 79.7 per-cent. (Results for students in specific incomegroups are: low-income, 80.4 percent; medium-income, 78.4 percent; and high-income, 82.9 per-cent.)

If we change the choice situation slightly toinclude college C (the third prior preference col-lege) and assume everything else is equal, thenthe estimated choice probabilities would be 71.8

percent, 18.2 percent, and 10.0 percent for thefirst, second, and 'fird prior preference colleges,respectively.

These examples clearly demonstrate the verystrong influence of prior preferences on choicebehavior. It takes a lot to overcome the inherentadvantage associated with being a student's first-choice prior preference college. This finding, ofcourse, means that it is important to examine thedeterminants of prior preference; this will bedone in Chapter 6.

Example 2: Prior preferences, financialaid, and choice probabilitiesWe now extend Example 1 and consider howscholarship aid might be used to offset the dis-advantage of not being the first-choice prior pref-erence college. We use the same basic situationas described in Example 1:

Choice setcompositionPrior preferencesituation

Financialconsiderations

College-specificconsiderations

Other relevantfactors

Two colleges, denoted as collegesA and B.College A is the first-choice priorpreference college alternative;college B is the second-choiceprior preference alternative.Colleges A and B are initiallyequal on COSTS, GRANTAID,and OTHERAID. However, asdiscussed below, college B will of-fer an "extra" scholarship.Colleges A and B are not topseven colleges (or, equivalently, itmay be assumed that they areboth average top seven colleges).Colleges A and B are equal onRENEWAL and SATFIT.

We now ask: How much extra scholarship aidabove and beyond that already offeredwouldthe second-preference college have to offer toincrease its chances of being chosen to 50 per-cent? Our results suggest that an extra scholar-ship of about $4,713 would be required. This re-

52 46

sult may be extended to our three income groups:low income, $3,175; medium income, $5,778;and, high income, $3,886. This illustrates the rel-ative sensitivity of the low- and high-incomegroups to scholarship aid, compared to the me-dium-income group.

As noted earlier, it is apparently possible to"buy" students to overcome toe disadvantage ofnot being the first-choice prior preference collegealternative; however, it does appear to be fairlyexpensive to do so.

Example 3: Scholarship aid and choiceprobabilitiesAnother view of the influence of scholarship aidon choice probabilities may be gained by exam-ining the influence of aid alone on choice, holdingeverything else constant. This situation is de-scribed as follows:

Choice setcompositionPrior preferencesituation

Financialconsiderations

College-specificconsiderations

Other relevantfactors

Two colleges, denoted as collegesA and B.Colleges A and B are equal inprior preference (i.e., tied forfirst-choice prior preference po-sition).

Colleges A and B are initiallyequal on COSTS, GRANTAID,and OTHERA1D. However, asdiscussed below, college B will of-fer an "extra" scholarship.Colleges A and B are not topseven colleges (or, equivalently, itmay be assumed that they areboth average top seven colleges).Colleges A and B are equal onRENEWAL and SATFIT.

This situation corresponds to a student facing atwo-alternative choice set where, considering allrelevant factors, the student is indifferent be-tween the two colleges. Thus, the probability ofchoosing each college is 50 percent: the studentis equally likely to attend either college. Another

interpretation of "indifference" (or 50-50 choiceprobabilities) is that this reflects our basic uncer-tainty about being able to predict which collegea student will ultimately choose.

Now, suppose that one of the colleges offersthe student an extra amount of scholarship aid(above and beyond the aid already offered). Ournext question is: How much would the choiceprobability shift if an extra scholarship awardwere offered? The shifts in choice probabilitiesfor various amounts of extra scholarship aid of-fered are shown in Table 4.17. As its illustrativecalculations indicate, large amounts of scholar-ship aid ($5,000) can move a 50-50 percent choicesituation to an 81-19 percent situation, when allother factors are held constant. However, a$5,000 extra scholarship would presumably haveto be renewed for an additional three years, thusrepresenting a total outlay of $20,000. Further-more, the $5,000 in extra scholarship really trans-lates into an effective cost of $13,039 per year.Here, effective cost is calculated as follows: prob-ability changes from 0.500 to 0.811 for $5,000 ofaid, so effective cost is (5000) (0.811)40.8110.500) = $13,039 per year, or $52,156 for fouryears (exclusive of the offset provided by tuitionfees).

The "holding other things constant" condition,the two-alternative choice set assumption, andthe assumption of equal prior preferences for thetwo colleges are all crucial to the interpretationof these figures. Later in this chapter we willinvestigate more realistic situations, in whichthese assumptions are relaxed.

Example 4: Financial aid andperceived renewabilityRenewability of financial aid is valued by ourhigh-ability students. Some trade-offs in size ofscholarship aid and degree of perceived renewa-bility are indicated by the data reported in Table4.18. If a college intends its financial aid to berenewable (perhaps under certain conditions of

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Table 4.17. Estimated effects of additional aid on choice probabilitiesAmount of extra scholarship

$o 81.000 82.000 83.000 14.000 85.000

Overall 50.0 57.2 64.1 70.5 76.2 81.1

Low income 50.0 60.9 70.9 79.2 85.6 90.2Medium income 50.0 55.6 61.0 66.2 71.0 75.4High income 50.0 60.0 69.3 77.2 83.6 88.4

Table 4.18. Effects of perceived renewability of aid

Amount ofschdarship offeredwith "possible- "Probable'.chance of renewal (RENEWAL =

Equivalent amount of scholarship that could be offered toobtain the same overall utility, with renewal perceived as:

-Certain-(RENEWAL, =

$4,000 $2,947 $1,893$4,500 $3,447 $2,393$5,000 $3,947 $2,893$5,500 $4,447 $3,393$6,000 $4,947 $3,893$6,500 $5,447 $4,393$7,000 $5,947 $4.893

academic periormance), then these figures sug-gest that this renewability should be clearly com-municated to students. Otherwise, students mayimplicitly downgrade or discount a financial aidoffer.

Example 5: SATFIT and financial aidEach extra point of SATFIT can be offset by ascholarship of $14. Thus, a 100-point SATFITvalue would require about a $1,400 scholarshipto just cover the lack of academic fit between thestudent and the college.

However, SATFIT is really an important factoronly for high-income students. For such students,the model predicts that each extra point of SAT-FIT may be offset by a scholarship of approxi-mately $29. Lower-tier colleges that seek to at-tract high-ability students must overcome the

lack of academic fit as well as other possibledisadvantages.

Toward a costbenefit analysis ofno-need aidWe now consider some further, more complicatedscenarios to illustrate the effects of using no-needfinancial aid. In realistic choice situations whereno-need aid might be offered by a college, wewish to assess the economics of using such aid.Our main concern is to document the costs as-sociated with pursuing such a pricing strategy.

The relevant costs associated with no-need fi-nancial aid include the actual amount of thescholarship aid for those who enroll at a collegedue to the aid, plus the costs associated with

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Table 4.19. Illustrative effective scholarship costs (costbenefit analysis 1)

Initial-year costsFour-yearscholarshipScholarship

Amount Expected Total extra cost per cost perof extra student scholarship incremental incrementalscholarship enrollment cost student student

$ 0 50.0 $ 0 $ 0 $ 0$1,000 57.2 $ 57,200 $ 7,944 $31,776$2,000 64.1 $128,200 $ 9,092 $36,368$3,000 70.5 $211,500 $18,317 $41,268$4,000 76.2 $304,800 $11,634 $46,536$5,000 81.1 $405,500 $13,039 $52,156

providing such aid to students who already wouldhave attended a college without any further no-need financial aid inducement. This latter groupis typically impossible to identify ahead of time,so no-need aid must be offered to a class of stu-dentsand not just those with low probabilitiesof attending a college in the first instanco.

Costbenefit analysis 1:A simple scenarioSuppose that a college offers no-need financialaid awards to each of 100 students who are ap-proximately indifferent between it and anothercollege (in the context of a two-alternative choiceset). Considering all relevant factors (exceptthese extra no-need financial aid awards), these100 students would split about 50-50 between thetwo colleges.

Wha- are the economics (in a costbenefitsense) of offering these students various amountsof no-need scholarship aid? Key numbers are dis-played in Table 4.19, for various amounts of no-need scholarships.

In interpreting t, aumbers in Table 4.19, it isimportant to note that:

The t-xtra no-need aid cannot be targeted spe-cificaliy at Jse who are very unlikely to attendthe no-need aid awarding college. All students

must be offered such aid, even those who wouldhave attended without it. (Of course, only someof these students will actually ultimately attendthe college offering the aid.)

The "four-year scholarship cost per incrementalstudent" assumes that the aid is continued forthe full four undergraduate years.

These calculations do not include the extra nettuition income generated by the "incremental"students responding to the no-need scholarshipaid.These results make clear that large no-needscholarships ($5,000) will:

Move many indifferent students toward the col-lege offering such aid (81.1 percent of such stu-dents will be induced to enroll, rather than only50 percent), and

Cost a substantial amount of money, when ex-pressed over a four-year time horizon ($52,156

per extra student attracted, before accounting forthe extra tuition income that these students willprovide).

Costbenefit analysis 2:A complicated (and realistic) scenarioA typical scenario involving the use of no-needaid is for a high-cost private college to offer suchfinancial support to compete more favorably with

. 49'.55

a low-cost public institution. Of course, otherconsiderations (such as perceived relative collegequality) may operate in favor of the private col-lege.

To investigate the economics of awarding suchaid, we will assume that the student in questionis high-income (so no-need aid is the only kind offinangial aid that could be offered) and:

College A College B(private) (public)

COSTSGRANTAIDRENEWALSATFIT

$12,000To be determinedGuc ranteed100

$5,000No aid offeredNot relevant150

All other variables mit ment"oned above are as-sumed to be equal for both colleges (excent whenmodified in the following discussion and analysis).

In this situation, the base choice probabilitywhen college A offers $0 of no-need aid is 42.8percent (assuming that colleges A and B areequally prefe-red on a print- preference basis).The disadvantage that college A faces with muchhigher costs is mly par.ially offset by a betterSATFIT 100 versus / 50). Some alternative situa-tions involving various amounts of no-need aid

and various prior preference situations are dis-played ir Table 4.20.

The last case described in Table 4.20 is partic-ularly noteworthy. The private college that usesno-need aid to compete with an otherwise pre-ferred (on a prior preferenre basis) public collegecan increase its choice probability from 13.3 to54.3 percent by offering $5,000 of no-need aid.However, this really represents an effective costper incremental student of $6,622 per year, or$26,488 over a four-year period (exclusive of tui-tion revenues from the student). Here, effectiv -cost per year in calculat( as follows: probabilitychanges from 0.133 to 0.543 for $5,000 of aid, soeffective cost Is (5000) (0.50/(0.543 0.133) =$6,622 per year, or $26,488 over four years.

The full set of effective costs associated withTable 4.20 are displayed in Table 4.21. The ex-treme costs of the necond case, where college Ais the first-choice prior preference college, arisebecause most of the students (78.4 percent) wouldhave attended the college with no extra no-needfinancial aid inducement. In contrast, the lastcase is relatively cost-effective for college A.Since few of the students would have attendedwithout the no-need aid, most of the aid goes to

Table 4.20. Illustrative probabilities (costbenefit analysis 2)Probability of choosing college A. if college A offers the following amountsof no-neeu scholarship aid

$0 $1,000

If colleges A and B areequally preferred on aprior preference basis

42.8 53.2

If college A is the first-choice prior preferencecollege

78.4 84.6

If college A is the second-choice prior preferencecollege

13.3 19.0

56

$2,000 $3.000 $4,000 $5.000

63.0 71. 9 79.3 85.2

89.2 92. 5 94.9 96.5

26.0 34.5 44. 2 54.3

50

Table 4.21. Illustrative effective costs (costbenefit analysis 2)Initial-year effective cost to college A of offering the following amountsof no-need scholarship aid

$1.000 $2.000 $3.000 $4.000 $5.000

If colleges A and B areequally preferred on aprior preference basis

$ 5.115 $ 6.238 $ 7.412 $ 8,690 $10.047

If college A is the first-choice prior preferencecollege

$12,645 $16.519 819.681 $23.006 $26.657

If college A is the second-choice prior preferencecollege

$ 3.333 $ 4,091 $ 4.882 $ 5,722 $ 6,622

students who actually switch (and little isawarded to those who would have attended with-out it).

Costbenefit analysis 3:Competition among top-tierand other private institutionsFor our next -;cenario, suppose that a lower-tierprivate institution wishes to compete against atop-tier private school for high-ability students.and that no-need aid is the chosen vehicle toimprove the lower-tier school's competitive situ-ation. Here, "top-tier" is defined as "top-seven"and "lower-tier" is defined to be not in the top-seven college group. What are the economics as-sociated with such competition?

Once again, we will assume that the student inquestion is high-income (so no-need aid is the onlykind of financial aid that could be offered) andthe factors shown below:

College A(the top-tierprivate college)

College B(the lower-tierprivate college)

COSTSGRANTAIDRENEWALSATFIT

$14,000No aid offeredNot relevant50

$9,000To be determinedGuaranteed150

In addition to the above, college A is presumedto be an average top-seven institution, while col-lege B is presumed not to be among the top-sevencolleges. All other variables not mentioned aboveare assumed to be equal for both colleges (exceptwhen modified in the following discussion andanalysis).

In this situation, the base-choice probabilitywhen college B offers $0 of no-need aid is 18.2percent (assuming that colleges A and B wereequally preferred on a prior preference basis). Asmay be noted, the value of college A being in thetop seven and the much better SATFIT (50 versus150) virtually overwhelm the advantage that col-lege B has on costs.

Some alternative situations involving variousamounts of no-need aid and various prior pref-erence conditions are displayed in Table 4.22. Inthis situation, note that if college B is not thefirst-choice prior preference college, there is vir-tually no chance of the student choosing to attendit (4.4 percent) in the absence of no-need aid. No-need aid, of course, will increase the choice prob-ability in favor of college B, but at considerablecost. The lower-tier private collegecollege B,in this examplethat uses no-need aid to com-pete with an otherwise preferred (on a prior pref-erence basis) top-seven private college can in-

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57

crease its choice probability from 4.4 percent to26.2 percent by offering $5,000 of no-need aid.Thus, even with a $5,000 scholarship offer, ourhypothetical student is still about three times aslikely to choose college A as college B (73.8 per-cent versus 26.2 percent). The $5,000 grant rep-resents an effective cost per incremental studentof $6,009 per student per year, or $24,036 perstudent over a four-year period (exclusive of tui-tion revenues from the student). Here, effectivecost per year is calculated as follows: probabilitychanges from 0.014 to 0.262 for $5,000 of aid, soeffective cost is (5000) (0.262)/(0.262 0.044) =

$6,009 per student per year, or $24,036 per stu-dent over four years. These results illustrate theoverwhelming advantage enjoyed by a top-sevencollege that is also a student's first-choice collegeon a prior-preference basis over a lower-tier pri-vate competitor. No-need aid will improve thelower-tier college's chances of attracting high-ability students, but large amounts are requiredto offset the advantage enjoyed by the preferredschool.

The full set of effective costs associated withTable 4.22 are displayed in Table 4.23. Onceagain, the effective costs associated with no-need

Table 4.22. Illustrative probabilities (costbenefit analysis 3)Probability of choosing college B. if college B offers the following amounts ofno-need scholarship aid

SO $1.600 $2.000 $3.000 $4.000 $5.000

If colleges A and 13 areequally preferred on aprior preference basis

18.2 25.3 33.7 43.3 53.4 63.3

If college 13 is the first-choice prior preferencecollege

52.0 62.2 71.2 78.7 84.8 89.3

If college 13 is the second-choice prior preferencecollege

4.4 6.5 9.5 13.6 19.1 26.2

Table 4.23. Illustrative effective costs (costbenefit analysis 3)Initial-year effective cost to college B of offering the follov:ing amountsof no-need scholarship aid

$1.000 $2.000 $3.000 $4.000 $5,000

If col!eges A and B areequally preferred on aprior preference basis

$3,563 $4.348 $5.175 $ 6,068 16 7,018

If college B is the first-choice prior preferencecollege

$6.098 $7.417 88.843 $10,341 $11,971

If college B is the second-choice prior preferencecollege

$3,095 $3.725 $4.435 $ 5,197 $ 6,009

eL- cip 52c.) 0

aid awards are largest when the initial situationis already favorable to a college. The effectivecost of no-need aid is minimized when it can betargeted to students who are unlikely to attendthe aid awarding college without the presence ofsubstantial no-need aid awards.

Cost-.5enefit analysis 4: The top-sevenprior preference phenomenonAs a final illustration of the economics of no-needaid, consider the case of a high-income studentwith an average SAT of 650. Assume a three-college choice set, as follows:

College A: First-choice prior preference college,costs = $15,000, no aid offered, an av-erage top-seven college, and average SATscore is 650 (so SATF1T = 0)

College B: Second-choice prior preference college,costs = $5,000, no aid offered, not a top-seven college, and average SAT score is500 (so SATF1T = 150)

College C: Third-choice prior preference college,costs = $10,000, aid to be determined,not a top seven college, and average SATscore is 500 (so SATF1T = 150)

This scenario describes the high-ability high-income student whose first-choice prior prefer-ence college is a top-seven college and whosesecond and third prior preference choices (col-leges B and C) are a local public college and alower-tier private college, respectively. In thisscenario, colleges B and C might be viewed bythe student as "safety colleges": they were orig-inally considered just in case the student failedto gain admission to the top-seven college.

In this scenario, colleges B and C are at atremendous disadvantage in not being "topseven," in not being the first-choice prior pref-erence college, and in having a poor fit in termsof SAT scores. College A is just right on SATF1T,and its only disadvantage is its high cost. Thisscenario seems to be a choice situation faced by

many students and one which is of interest inillustrating the importance of first-choice priorpreference, of being a top-seven college, and ofSATF1T, even for a college with costs of $15,000.

If college C gives $0 of no-need aid, then thechoice probabilities are: college A, 94.4 percent;college B, 4.5 percent; and college C, 1.0 percent.Thus, with $0 no-need aid, college C stands vir-tually no chance of attracting this student. On theother hand, if college C discounts its cost to thisstudent by 50 percent by a guaranteed renewable$5,000 grant, the choice probabilities change to:college A, 88.4 percent; college B, 4.2 percent;and college C, 7.5 percent. The effective cost ofthis $5,000 no-need aid award to college C is(5,000) (0.075)1(0.075 0.010) = $5,769 per stu-dent per year (exclusive of tuition).

If college C provides a guaranteed renewable,full-cost scholarship of $10,000 (i.e., reduces itscost to $0 for four years), the choice probabilitiesshift to: college A, 59.0 percent; college B, 2.8percent; and college C, 38.2 percent. This wouldrepresent an effective cost of (10,000) (0.382)/(0.382 0.010) = $10,269 per student per year,exclusive of tuition. (Note that this last example,with $10,000 of no-need aid, is somewhat specu-lative, as a grant of $10,000 would be an extremedata point based on our sample data, and we can'thave a lot of confidence that the model estimatesare highly accurate at such extremes.)

College C is unlikely to attract students in thechoice situation described here under any con-ditions. However, there is very little risk of givingmoney to students who are going to attend any-way. Thus, the incremental cost per student forthe small proportion of students induced to enrollis not much more than the actual value of thescholarship. However, to use this result in prac-tice, college C would need a way to target its half-or full-cost grants to students with choices likethe one illustrated here. Also, even though col-lege C would not pay much more than the actualscholarship cost per incremental student (assum-

53.

59

ing it could find some way to target aid to unlikelyprospects), presumably it cannot give very largeno-need scholarships to substantial numbers ofstudents.

Alternatively, of course, college C might at-tempt to improve the quality of its college (e.g.,improve faculty and academic facilities), whichmight ultimately serve to attract a mo able stu-dent body (see the results in Chapters 6 and 7 foranalysis of the factors which influence , ior -;;ef-erence). Rather than use no-need aid, collegecould invest an equivalent amount in 11. provingthe rest of its academic enterprise.

ConclusionsThe purpose of this chapter was to estimate astatistical model of the college choice decision-making process. Using the multinomial logitmodel, we developed and estimated such amodel. The main results of this exercise are a setof estimated relative-importance weights that in-dicate how our high-ability students weighed thevarious factors at work in the college choice de-cision.

Our findings indicate that college choice for ourhigh-ability high school students is a complicateddecision process. Many factors are weighed andconsidered. There is no single way to describethe relative importances which students employin college choice decision-making; many thingsmatter. A concise summary of these findingsmight be that students choose colleges primarilyon the basis of their prior preferences, and thataid plays a role in the choice process, especiallyguaranteed renewable scholarship aid.

The estimated relative-importance weightsseem remarkably stable and consistent across arange of demographic variables and choice situ-ations. There appear to be no systematic differ-ences in these weights based on average SATscores, gender, planned educational level, andplanned major field of study, although some dif-

ferences based on parental income levels are ob-served. Also, the concentration of top-tier privateschools in students' choice sets does not seem tosystematically influence the choice weights.

The following specific conclusions that may bedrawn from the findings reported in this chapter:

Prior preference is the primary determinant ofcollege choice behavior.

Financial considerations are relevant, but are ofsecondary importance to prior preference.

Scholarships are viewed positively by students;other aid (loans and part-time jobs) are viewedneither positively nor negatively by students.

Institutional costs detract from the overall at-tractiveness of a college. This effect becomes lessimportant to students as their income increases.

"Buying" students with no-need aid is possiblebut costly. It is especially difficult to change stu-dents' decisions when they begin with a priorpreference for another college alternative.

Students implicitly penalize a college if they areconsiderably more academically able than the av-erage student at the college. Students prefer toattend colleges where the students are, on aver-age, fairly close to their own level of ability. Thischoice factor operates primarily for high incomestudents.

Renewability of aid is important to students.Students implicitly penalize a college awardingnonrenewable aid by downgrading the amount ofthe aid. Of course, receiving nonrenewable aid ispreferred to receiving no aid at all. This implicitdiscounting is especially evident for low-incomeand, to a lesser extent, mcdium-income students.

Given the importance of prior preference sta-tus, Chapter 6 investigates in detail the deter-minants of prior preference. Details about thefinancial aid awarding behavior of colleges will beanalyzed in Chapter 5.

60

5. Determinants offinancial aid awards

Findings presented in the preceding chapter es-timate the influence of monetary factors (collegecosts and financial aid) on the college choices ofhigh-ability students. This chapter is concernedwith the criteria used by colleges in allocatingfinancial aid. To what degree is financial aidbased on considerations of academic merit ratherthan on financial need? Evidence from prior re-search concerning colleges' use of criteria otherthan need in allocating aid, and evidence drawnfrom data in this study, are summarized below.

BackgroundVenti, in a chapter in Manski and Wise (1983),estimated the relative influences of a number ofstudent and college characteristics in accountingfor allocation of discretionary grant aid by thecolleges attended by students in the 1972 Na-tional Longitudinal Study. Based on his findings,Venti concluded that "variables measuring need(particularly income and tuition) and variables re-lated to merit (particularly class rank and SAT)are of roughly equal importance in determiningaid offers" (p. 103). This conclusion was basedon simulated changes in aid as indicated by amathematical model fit to the NLS data. Ventiestimated, for example, that differences of ap-

proximately two standard deviations in total SATscores (360 points), in parents' income ($11,640),and in college tuition (about $1,650) would resultin the following changes in aid dollars for studentsenrolled in four-year colleges: student SAT, $810;parents' income, $876; and, college tuition,$965.

Further information concerning use of meritcriteria in awarding aid and trends over the ten-year period 1974-84 can be obtained from a seriesof surveys of institutional financial aid practices.Relevant surveys include (1) a 1974 survey byHuff published in the College Board Review in1975 (Huff 1975); (2) a 1977 survey concernedspecifically with no-need aid awards (Sidar andPotter 1978); (3) a 1979 survey of admissions pol-icies and practices conducted by the CollegeBoard and the American Association of CollegiateRegistrars and Admissions Officers, which in-cluded questions relating to no-need aid awards(College Board/AACRAO 1980); (4) a 1982 surveyconcerning institutional use of no-need aid (Por-ter and McColloch 1982); and (5) a 1964 surveyof undergraduate need-analysis policies, prac-tices, and procedures conducted by the CollegeBoard and the National Association ol StudentFinancial Aid Administrators (College Board/NASFAA 1984).

Although differences in populations of institu-tions surveyed and in definitions of no-need fi-nancial aid make the findings of these surveysdifficult to compare, the results show a generally

55 61

Table 5.1. Summary of publishedresearch on use of no-need awardsin aid decisions

Regponding four-year institutionsreporting use of no-need criteria inawarding aid (7(1

Public Private

HuffI974 54 55

Sidar and Pottcr-1977 64 74

College BoardIAACRAO-1979 60 61

College Board/NASFAA-1984 90 85

consistent pattern of a high and increasing inci-dence of use of no-need aid awards (see Table5.1 for a summary of the key findings with regardto the incidence of no-need awarding).

Sidar and Potter (1978) included tuition remis-sions for children of a college's faculty and staffmembers in their definition of no-need aid, whichmay account in part for the higher incidence re-ported in their study than in other surveys takenat a similar time.

The 19i 2 Porter and McColloch study does notprovide directly comparable figures. However. 25percent of institutions responding to this surveyre,,r)rted providing financial recognition for aca-G Aie excellence to 1 percent or less of freshmen.This implies a lower bound estimate of 75 percentof four-year institutions giving no-need aid in1982. a result consistent with the trends shownin Table 5.1. Several features of no-need aid re-ported by institutions responding to the 1984 Col-leg. Board/NAM:AA survey are summarized inTable 5.2.

Results of these surveys of college concerningaid policies and pract5ces confirm informal re-ports and the perceptions of admissions and fi-nancial aid officers that increasing numbers ofinstitutions award a portion of financial aid tostudents on the basis of academic eriv..ria.cording to the College Board/NASFAA study,

62

many of the awards are less than $1,000an es-timated 80 percent at four-year public institutionsand an estimated 50 percent at four-year privateschools. However. some awards are appreciablylarger. Four-year private colleges report that 20percent Of their no-need scholarships exceedS2.000 and 6 percent exceed 84.000.

Incidence and magnitude of aidoffers to students in this studyThe 1.183 students with whom telephone inter-views were completed in our study received 3.988admissions offers. Of the 1.183 students, 754 (64percent) were offered financial aid by at least onecollege. Of the total 3.988 admissions offers,1,486 (37 percent) were accompanied by offers offinancial aid. The average total aid package (in-cluding grant, loan, and job aid) was $4,810, ahigh figure reflecting the fact that a substantialnumber of admissions and aid offers to studentsin our sample were from high-cost institutions.The average college cost for colleges making the1,486 aid offers was $11,062.

The breakdown of aid offers to students in oursample among grant, loan, and job aid is shown

Table 5.2. No-need aid characteristicsFour-yearpublic

Four-yearprivate

Average number of awards 241 104

Average value of awards $835 $1.558

Percent renewable 45% 72%

Distribution of awards:under $500 35% 13%

$ 500$1.000 45 37

$1,000$2,000 17 29

$2,000$3,000 1 11

$3,00044,000 3

$4,000 or more 1 6100% 100%

56

Table 5.3. Some financial aidstatistics

Type of aid award

Percentage of financialaid offers thatincluded such aid

Grant aidLoan aidPart-time work aid

91.445.136.2

Renewability of financial aid offers

Average

financialaid award

$3.674$2,081$1.125

Possibility of aidbeing renewed Percentage

No responseNo possibilityPossibleProbableDefinite

11.04.8

18.954.910.3

100.0%

Note: The "average financial aid award- numbers refer to allthose awards greater than $O.

in Table 5.3, as is reported renewability of finan-cial aid offers. Most students who received col-lege-specific financial aid reported that the like-lihood of its renewal was "probable" (54.9 percent)or "definite" (10.3 percent). Only 4.8 percent re-ported that specific aid offers had "no possibility"of renewal.

These high-ability high school students re-ceived considerable amounts of portable financialaid from such sources as state scholarship ro-grams, ROTC, National Merit, and other privatescholarship programs. Such portable financial aidis defined to be scholarships awarded to the stu-dent by noncollege sources, which may be usedby a student at any college of his or her choosing.Some relevant descriptive statistics regardingportable financial aid are displayed in Table 5.4.Almost half (49.0 percent) our students reportsome portable financial aid. The predominantsource of this aid is the National Merit Scholar-ship Corporation (32.1 percent). Those students

with portable financial aid reported an averageamount of 81.229. About half _his personal finan-cial aid is not renewable (50.6 percent).

Determinants of aid offersIn response to interview questions concerning no-need aid, a total of 572 student:, 48 percent ofall students interviewed and 76 percent of thoseoffered any aid-stated that one or more collegeshad offered aid based in whole or in part on ac-

Table 5.4. Portable financial aidaward statisticsIncidence of portable aid

Students with portable aid 49.0%Students with no portable aid 51.0

100.0%

Sources of portable financial aid awards

National Merit Scholarship 32.1%Community organization 18.1Regents 11.1Corporation 11.1State government 6.3ROTC 3.8Corporate merit scholarship 3.1National Honor 0.9Labor union 0.6Other 12.4

100.0%

Amounts of portable financial aid awards

AverageMinimumMaximum

= $ 1,229= $ 25

= $11,000

Possibility of renewal of portable financial aid awards

Don't knowNonePossibleProbableGuaranteed

5763

1.5%50.6

6.923.117.0

100.0%

ademic considerations. This high level of report-ing by a sample of academically able students ofaid offers based on academic criteria is not sur-prising in light of the information on institutionalpractices summarized at the beginning of thischapter.

Institutions use of other than need-based cri-teria in atianling financial aid was also evident inthe extent tr., which students reported receivingaid offers from colleges to which they had notapplied for financial aid. Table 5.5 shews (for the3,988 admissions offers) the incidence of aidawards to (a) students applying for aid and (b)students not applying for aid at the college offer-ing admission. Naturally, aid is offered more oftento those who apply for it. However, the fact that14 percent of the offers of admissions to studentsnot applying for aid included aid awards providesfurther evidence concerning the extent that no-need criteria are used in awarding aid.

Apart from data on college admissions and aidoffers, information was available for many stu-dents in the study sample concerning family fi-nancial circumstances, academic ability, andother variables expected to have a relationship tothe incidence and magnitude of financial aid of-fers_ Relevant data on colleges making admis-sions and aid offers (such as information on col-lege r,st.-..) was also available. These data allowedub ,--.4anEine statistically the extent to whichneed and merit criteria account for aid awardsreported to us by students.

in carrying out these analyses, it was judgedimportant to examine separately certain groups

Table 5.5. Incidence of aid awardsApplied for aid

of colleges for which there were a priori reasonsto expect need and merit criteria to be differen-tially weighted in aid decisions. A number of themost highly selective colleges in the United Stateshave stated policies of awarding aid on the basisof need only, with exceptions in certain of thesecolleges for a small number of special scholar-ships. No-need scholarships were expected to beused more frequently by colleges below the high-est levels of academic reputation. A smaller pro-portion of these colleges subscribe to policiescalling for allocation of financial aid on the basisof need only. Furthermore, colleges below thehighest levels of academic reputation are ex-pected to use financial incentives more frequentlyin competing with thc most selective colleges forhighly able students.

In studying determinants of aid awards, wedivided colleges named by students into threegroups, using a proxy measure of academic rep-utation identified for purposes of this study as theAQSCORE (see Chapter 7 for a discussion of thedevelopment of this index and its components).The high AQSCORE group consisted of collegeswith AQSCOREs higher than one standard devia-tion above the mean of this index; the middlegroup consisted of colleges with AQSCOREs be-tween the mean and one standard deviation abovethe mean and the low group consisted of thosecolleges with AQSCOREs below the mean. Thenumbers and percentages of colleges in eachgroup, and the percentages of all admissions of-fers to students in the sample made by collegesin each group are shown in Table 5.6.

Did not apply for aid Total

Number Percentage Number Percentage Number Percentage

Aid offered 1,251 54 235 14 1.486 37

Aid not offered 1.078 46 1.424 86 2.502 63Total 2.329 100 1.659 100 3.988 100

64 58

Table 5.6. Colleges' admissions offers by academic reputation groupNumber ofcolleges

Percentageof colleges

Percentage ofadmissions offers

High AQSCORE group 83 15% 50%Middle AQSCORE group 186 34 32Low AQSCORE group 281 51 18

100% 100%

The high percentage of admissions offers bythe high AQSCORE group (which contains themost highly selective colleges) reflects the factthat this group of colleges received, on average,far more applications from students in our samplethan did colleges in the other groups. This is afurther indication of the relative attractiveness ofsuch colleges to students like those in our sample.

The relationships of aid offers to student andcollege characteristics were studied separatelyfor students applying for aid and for those notapplying for aid to colleges within each of thesethree college groups. That is, each admissionsoffer was assigned to one of six groups:

High AQSCORE group, aid applied forMiddle AQSCORE group, aid applied forLow AQSCORE group, aid applied for

High AQSCORE group, aid not applied forMiddle AQSCORE group, aid not applied forLow AQSCORE group, aid not applied for

Within each group, the probability that an ad-missions offer would be accompanied by an aidoffer was examined as a function of (1) studentfinancial need as measured by college costs andexpected family contribution and (2) academicability as measured by SAT scores. Since the de-pendent variable for this analysis was dichoto-mous (1 if aid was offered, 0 if aid was not of-fered), logistic regression methods were used.

Direct measures of expected family contribu-tion to college costs were available for studentswho had filed with the College Scholarship Ser-

vice (CSS). Of the total 3,988 admission offers,more than 2,400 involved students with CSS-com-puted family contributionsprimarily studentsapplying for aid at one or more colleges. We alsohad available from response to the Student De-scriptive Questionnaire (SDQ) student-reportedinformation on several key variables included inthe CSS computation: family income, plrents'number of dependents, and number of other de-pendents in college during the student's first year.Regression analyses of CSS-contribution figureson these SDQ responses (or functions of theseresponses) allowed development of a weightedindex for imputing family contributions from suchresponses. The correlation of values of thisweighted index with CSS figures was 0.65. Of the3,988 admission offers, 3,478 were to students forwhom family contributions could be imputed. Be-cause the incidence of finIncial aid awards wasto be studied both for aid applicants and for stu-dents not applying for aid, family contributionsimputed from SDQ responses (rather than CSSfigures) were used throughout in the modeling ofaid award incidence.

Table 5.7 gives the estimated parameters of thelogistic regression models for aid incidence foraid applicants and for aid non-applicants in eachof the three college groups. Generally the findingsconform to prior expectations.

Aid applicantsFor aid applicants in the high AQSCORE group,th, effects of college costs and imputed familycontribution are large and statistically significant.

59 65

Table 5.7. Estimated parameters of logistic regression models for aidincidence (offered vs. not-offered financial aid)

College quality groups

High AQSCOREgroup

Coeffi- T-Ratiocient

Middle AQSCORE Low AQSCOREgroup

Coeffi-cient

group

T-Ratio Coe& T-Ratiodent

Aid applicantsCollege costs

(in $000s)0.0652 2.75* 0.1610 6.60* 0.1805 4.55*

Imputed familycontribution(in $000s)

0.1590 9.92* 0.0505 2.76* 0.0249 1.08

Average SATscore (V and M)

0.0013 1.01 0.0057 4.41* 0.0053 3.12*

Constant term 0.0739 4.8037 4.3446

Nonaid applicantsCollege costs

(in $000s)0.1512 4.48* 0.0280 0.72 0.1060 1.98

Imputed familycontribution(in $000s)

0.0240 0.71 0.0730 2.71* 0.0435 1.39

Average SATscore (V and M)

0.0133 4.12* 0.0070 3.55* 0.0119 4.19*

Constant term 10.3641 5.8152 9.0969

Note: An asterisk denotes coefficients that are statistically significant at the 1 percent

The coefficient for SAT scores is positive, but itis small and not statistically significant. Need cri-teria are clearly predominant in accounting forincidence of aid awards to aid applicants in thisgroup.

For aid applicants in the middle AQSCOREgroup, the effects of college costs and imputedfamily contribution are statistically significant,though family contribution has a weaker effectthan in the high AQSCORE group. In this group,the effect of SAT scores on incidence of aid offersis large and statistically significant.

For aid applicants to colleges in the low

66

level.

AQSCORE group, college costs and SAT scoreshave large and statistically significant effects.The sign of the coefficient for imputed familycontribution is in the expected negative direction(students from families with higher expected con-tributions are less likely to be offered aid), butthe coefficient is small in absolute value and isnot statistically significant.

In summary, different factors account for theprobabilities of aid awards from colleges in thethree groups to aid applicants in our sample. Inthe high AQSCORE group, need-based criteriapredominate. In the middle group, need and

60

merit criteria are both important. In the lowgroup, academic ability is important, and im-puted family contribution has a small effect onthe probability of an aid offer.

It should be noted that these findings applyonly to students like those in the population wesampled fromin particular, students with aver-age SAT scores of 550 and above. Such studentshave academic credentials that are far strongerthan those presented by most applicants to manynonselective colleges. Although imputed familycontribution does not discriminate well betweenaid applicants in our sample who were and werenot offered aid by colleges in the low AQSCOREgroup, it might well have a stronger effect onincidence of aid offers to the larger population ofadmitted students in these colleges.

Nonaid applicantsFor students not applying for aid, SAT scores hada strong and statistically significant positive effecton the probability that a student would be offeredaid within each of the three college groups.Clearly, aid offers to nonaid applicants arelargely predicated on evidence of academic abil-ity.

College costs had a statistically significant neg-ative effect in the high AQSCORE group on prob-ability that nonapplicants would be offered aid,in contrast to the observation for aid applicantsthat the probability of aid increased (as expected)with increasing college costs. This finding sug-gests that the practice of offering aid to studentsnot applying for it is more common among rela-tively low-cost colleges within the high AQSCOREgroup.

Imputed family contribution had a statisticallysignificant negative effect on the probability of anaid award to a student not applying for aid forcolleges in the middle AQSCORE group. It ap-pears that these colleges use both need and ac-ademic criteria in deciding to offer aid awards tononaid applicants. Perhaps this form of aid is

targeted to able students from families judged tohave a relatively high degree of difficulty in meet-ing college costs and who might therefore be moreresponsive to differences in net college costs pro-duced by aid offers.

While colleges in all three groups offered aidto students who had not applied for it, and whileacademic criteria appeared to be used predomi-nantly in allocating these awards, there werestrong differences among the three college groupsin the extent to which aid was offered to aon-applicants. To illustrate, the models for aid inci-dence provide the following estimates of proba-bilities that a nonaid applicant with an imputedcontribution of $10,000 and average SAT scoresof 650 will be offered aid by colleges with costsof $10,000 in each of the three groups: 0.05 in thehigh AQSCORE group, 0.15 in the middleAQSCORE group, and 0.32 in the low AQSCOREgroup.

Table 5.8 provides illustrative estimates ofprobabilities that aid applicants and nonappli-cants with certain combinations of SAT scoresand imputed family contributions will be offeredaid at colleges in each of the three groups. Forthese illustrations, college costs have been heldconstant at an assumed total cost of $10,000. Thevalues calculated in these illustrations should notbe taken as precise estimates of the actual prob-abilities that students with the given SAT scoresand family contribution values will be offered aidat any given college. The estimates are differentthan they would have been had actual CSS con-tribution figures (rather than an index correlatedwith the CSS values) been used in the analyses,and they were derived by aggregating across col-leges. Furthermore, they cannot account for ad-justments individual colleges may make in needcalculations. These illustrations are presentedprimarily to highlight relative changes in aid prob-abilities in response to SAT and family contribu-tion differences for aid applicants and nonappli-cants in the three college groups.

61 6 7

Table 5.8. Estimated probabilities of aid offers (for collegeswith total costs of 810,000)

Imputed

Aid applicants'SAT scores

Non-aid applicants'SAT scores

contribution 550 650 750 550 650 17.0

High AQSCORE groupLow ($ 1,000) .78 .80 .82 .01 .04 .13Medium (S 5,000) .66 .68 .71 .01 .04 .14High ($10,000) .46 .50 .53 .01 .05 .16

Middle AQSCORE groupLow ($ 1,000) .47 .61 .74 .15 .26 .41Medium ($ 5,000) .42 .5f) .70 .11 .21 .34High ($10,000) .36 .50 .64 .08 .15 .26

Low AQSCORE groupLow (5 1,000) .59 .71 .80 .18 .41 .70Medium (S 5.000) .56 .69 .79 .15 .37 .66High ($10,000) .53 .66 .77 .13 .32 .61

Table 5.9 shows the changes in aid probabili-ties implied by each of the six models that areassociated with the following differences in im-puted family contribution and in SAT scores:1. A reduction in contribution from $10,000 to$1,000 (holding SAT scores constant at 650 andcollege costs constant at $10,000), and2. An increase in SAT scores from 550 to 750(holding the contribution constant at $5,000 andcollege costs constant at $10,000).

These differences provide specific illustrationsof certain of the main conclusions just summa-rized. It is clear that relatively large changes in aidprobabilities are associated with differences inestimated family contributions for aid applicantsto colleges in the high AQSCORE group. Suchchanges are also associated with differences inSAT scores for both aid applicants and nonappli-cants in the middle and low AQSCORE groups.All other differences in this illustration are smallin practical terms.

68

Aid amounts in excess of calculatedneed

The preceding section focused on incidence ofaid offers without respect to the amounts of aidoffered. In this section, we discuss the results ofanalyses comparing total aid offers to calculatedfinancial "need." For this purpose, calculatedneed was taken to be the difference between totalcollege costs and the CSS estimate of expectedfamily contribution toward these costs. (For theseanalyses, it was deemed important to use theactual CSS figures rather than imputed values,and the analyses therefore are limited to CSSfilers.) If the difference between the total dollaramount of an aid offer and the need calculatedas previously defined was positive, the offer wasconsidered to exceed need. If this difference waszero or negative (or if no aid was offered), thecase was classified as one in which aid did notexceed need.

62

Table 5.9. Illustrative changesin aid probabilities

Estimwd change in aidprobability associated with

Contributiondifference

SATdifference

Aid applicantsHigh AQSCORE group .30 .05Middle AQSCORE group .11 .28Low AQSCORE group .05 .23

Nonaid applicantsHigh AQSCORE group .01 .13Middle AQSCORE group .11 .23Low AQSCORE group .09 .51

Even if colleges awarded aid based only onfinancial need, we would not expect aid figuresto match precisely our calculated need figures forall students. Apart from possible errors in ourfinancial aid data for some students, discrepan-cies would arise from the fact that colleges adjustthe CSS figures in forming their own estimates ofneed and from the fact that different total ex-pense budgets may be appropriate for differentstudents. For these reasons, we will focus atten-tion on patterns in the data (rather than on ab-solute differences) and on the degree to which aidexceeding "need" is related to other ,ariables.

Table 5.10 shows by AQSCORE group and byinterval on SAT score the number of admissionsoffers to CSS filers, the percent of these accom-panied by aid offers greater than calculated need,and the distribution of this "excess aid" in dollarsover several intervals. Within each college group,the percentage of offers in excess of need clearlytends to increase with increasing SAT scores.(Curiously, however, students in the 650-699 and700-749 SAT intervals have about the same per-centage of offers in excess of need within eachcollege group.) To illustrate the range of differ-

ences, the following chart contrasts the percent-ages of students in the lowest and highect SATintervals offered excess aid by colleges in eachof the three groups.

SAT score interval

550-599 750-800

High AQSCORE group 4 25Middle AQSCORE group 13 33Low AQSCORE group 17 46

Holding SAT score interval constant, percent-ages of excess awards also increase as one movesfrom the high to the middle to the low AQSCOREgroup. Consistent with the findings on aid inci-dence described above, these results suggest thatcolleges in lower AQSCORE groups weight aca-demic criteria more heavily than those in highergroups in determining amounts of financial aidawards.

While Table 5.10 presents results descriptively,it should be noted that the effects of college groupand SAT score interval were tested formally inlog-linear analyses. Likelihood-ratio tests indi-cated that both these factors and their interactionwere statistically necessary (at levels of signifi-cance beyond 0.0001) to account for cell frequen-cies in the table.

Despite the differences among college groupswhen SAT scores c.re held constant, it is worthyof note that the overall percentages of awards inexcess of need to students in our sample withoutrespect to S AT scores are similar for the threegroups, ranging from 21 percent to 25 percent.This similarity arises because the colleges in thehigher groups have proportionately larger num-bers of admitted students in the higher SAT in-tervals where excess aid offers are relatively morefrequent. From this perspective, it could be ar-gued that the evidence suggests tnat colleges inthe three groups respond somewhat similarly toacademic criteria in determining aid offers in ex-ceos of need, but that this responsivenes is a

63 6 9

Table 5.10. Percentages of aid offers exceeding calculated needNumber ofadmissionsoffers

Percentage withaid offers abovecalculated need

Percentage with offers exceeding need by:

$3.000+$141.000 $1.001-52.000 $2.001$3.000

High AQSCORE group

550-599 48 4 0 2 0 2

600-649 132 15 7 2 3 3

650-699 211 19 9 2 4

700-749 325 18 9 2 4 3

750-800 461 25 5 5 5 10

Total 1.177 21 7 4 4 6

Middle AQSCORE group

550-599 144 13 4 5 1 3

500-649 173 15 7 2 3 3

650-699 173 25 12 5 3 5

700-749 156 22 10 3 5 4

750-800 153 33 10 8 5 10

Total 799 22 9 5 3 5

Low AQSCORE group

550-599 142 17 8 5 2 2

600-649 117 22 10 3 3 6

650-699 82 31 16 9 1 5

70(1-749 53 29 9 8 8 4

750-800 46 7 10 13 6

Total 442 25 11 6 4 4

function of the academic ability of a student rel-ative to the distribution of academic ability in thepool of admitted students. Students with SATscores of 750-800 accepted to colleges in the highAQSCORE group, students with scores of 6L0-699accepted to colleges in the middle group, andthose with scores of 600-649 accepted to collegesin the low group have similar chances of beingoffered aid in excess of calculated need. Althoughthese students differ in absolute SAT scores, theirrelative standings in the pools of admitted stu-dents in each college group are no doubt moresimilar.

The results summarized in Table 5.10 also sug-gest that for the high and middle college groups,

particularly high awards are offered relatively fre-quently to students in the highest SAT interval(750-800). For both of these groups, 10 percentof CSS filers with scores in this intervt ' reportedaid awards exceedin6 calculated need by morethan $3,000. This finding may reflect the prActiceof certain colleges in these groups of awardinglarge merit scholarships (so,fle equal to full tui-tion) to small numbers of students with verystrong academic credentials.

SummaryOur findings relating to the determinants of fi-nancial aid awards are highly consistent with

70 "

other informatior and institutional self-reportsconcerning policies on the allocation of financialaid.

Colleges at the highest levels of academic rep-utation appear io rely primarily on informationconcerning student financial need in decidingwhether to offer financial aid to students whohave applied for it. However, it is evident thatsome colleges in the highest group defined forthis study (generally lower-cost colleges withinthis group) make aid offers to students with strongacademic credentials who have not applied foraid. It is also evident that even in this highestgroup, increases in SAT scores we associatedwith greater probabilities that students will beoffered aid exceeding calculated financial need.

In general, colleges ranked lower on an indexof academic reputation are far more responsiveto students' academic ability than are higher-ranked colleges in determining farancial aidawards. Strikingly, in the lower two collegegroups defined for this study, the probability astudent would be offered aid 'varied by only asmall amount in response to large changes inimputed family contribution to college costs.while this probability varied by much largeramounts in resporse to increases from 550 to 750on the SAT. Moreover, the percentages of stu-dents receiving aid offers in excess of need fromcolleges in these groups increase sharply withincreasing SAT scores.

'65 71

6. Antecedents of college choicebehavior: Preference judgmentformation

Preference judgment formation, the immediateantecedent of choice behavior, is analyzed in thischapter. An antecedent of both choice behaviorand preference judgment formationperceptionjudgment formationwill be analyzed in Chapter7. Given the results in Chapter 4, prior preferenceis of crucial importance in explaining collegechoice behavior. We seek to examine and analyzethe determinants of prior preference formation inthis chapter. In our multistage college choicemodel, prior preference is postulated to dependon a student's perceptions of the college alter-natives.

Development of perceptual ratingsindicesTo describe college alternatives in terms of stu-dents' perceptions, we construct composite per-ceptual ratings indices. Factor analysis proce-dures are used to assess the underlyingcorrelation pattern in our perceptual ratingsscales. Then, four key composite perceptual rat-ings indices are developed. The details of thisindex construction are described in this section.

Definitions of the 14 raw perceptual ratings

used in this study are displayed in Table 6.1.These definitions are the actual phrases used inthe survey research questionnaires. The 14 scaleswere developed with reference ',o previous re-search on the determinants of college choice be-havior. The main sources consulted were Astin,et al. (1983, 1984, and 1985), Chapman (1977,1979), Kohn, Manski, and Mundel (1976), Littenet al. (1983), and Manski and Wise (1983).

These 14 perceptual ratings were collected onthe following grading scale: A = "excellent"; B= "good"; C = "fair"; D = "poor"; and, F ="unacceptable." For analysis purposes, these let-ter grades were transformed into a 1-5 numericalscale, where 1 = "F" and 5 = "A."

These 14 perceptual ratings of each collegepresumably represent fewer than 14 completelyseparate and distinct aspects of colleges. Eventhough an attempt was made to have them rep-resent relatively distinct dimensions on collegefeatures, correlation among the ratings is inevi-table, if for no other reason than the presence ofcross-scale halo effects. Thus, it is appropriateto seek a reduced-space representation of theseperceptual ratings scales.

Standardization transformationsIn seel% ing to construct a perceptual space todescribe the perceived positioning of colleges, anumber of issues of data scaling arise with regardto the college ratings provided by the survey re-

7266

Table 6.1. Definitions of perceptual ratings used in this studyVariable Definition

DIVERSITYFACILITIESGEOLOCATEREPUTATIONLOWCOSTSOCIALFITSPECPROGCOMMUNITYPREPGRADAIDAVA1LCONTACTACADSTRNUGRADEMPEXTRACUR

Academic diversity irange of courses offered)Academic facilities (library, computer resources, laboratories, etc.)Geographical location (part of the country, distance from home)Overall academic reputationLow overall costs (cuition. fees, room and board, other expenses)Social climate (college atmosphere. what the student body is like. how you would fit in)Availability of special majors, degrees. or honors programsCommunity setting (urban, suburban, small town. rural)Preparation for career or graduate and professional school opportunitiesAvailability of financial aidPersonal contact with college representatives (admissions staff. faculty. coaches. others)Academic strength in your major areas of interestEmphasis on undergraduate education (small classes. faculty contact. etc.)Opportunities for involvement in extra-curricular activities (clubs, sports, performing arts,journalism, etc.)

spondents. These issues concern ratings varia-bility across attributes and respondents (see Dil-lon. Frederick. and Tangpanichdee 1985 for a

review of these issues).The specific scaling adopted here follows the

suggestion of Dillon, Frederick, and Tangpanich-dee (1985, pp. 57-58). In particular, the raw rat-ings data were standardized to highlight thewithin-respondent variance on the attribute rat-ings over the colleges rated by each respondent.Each attribute was standardized (to mean zeroand variance one) across the colleges rated foreach respondent separately. That is, the ratingson the first attribute for the first respondent overthat respondent's colleges were transformed tohave mean zero and variance one. This procedurewas repeated for the second and subsequent at-tributes of the first respondent, ultimately result-ing in all the ratings data for the respondent beingstandardized to mean zero and variance one foreach attribute. This procedure was then repeatedfor all respondents. As summarized by Dillon,Frederick. and Tangpanichdee: "The standardi-

zations within each 1.espondent will remove fromthe analysis the variance on the attribute char-acteristics clue to individual level effects. Theremaining variance gives the interrelationshipsbetween changes in the attribute characteristicsover the brands generalized across the respond-ents."

Redundancy structureamong the perceptual ratingsThe correlations in the standardized perceptualratings are displayed in Table 6.2. The correla-tions between the various perceptual ratingsscales may be noted to be relatively modest.There are only a few values greater than 0.35 inabsolute value. Still, further analysis is necessaryto determine whether it is possible to representthese 14 perceptual ratings in a more compact,simpler fashion.

In an attempt to reduce these 14 perceptualratings to a more manageable and interpretablenumber, a principal components factor analysiswas conducted. The results of the -varimax rota-

73

Table 6.2. Correlations among the 14 (standardized) perceptual ratings scalesNo. Variable 2 3 4 5 6 7 8 9 10 11 12

2031

01

3317

0531

04390002

13 14

1

23456789

1011

1213

14

DIVERSITYFACILITIESGEOLOCATEREPUTATIONLOWCOSTSOCIALFITSPECPROGCOMMUNITYPREPGRADAIDAVAILCONTACTACADSTRNUGRADEMPEXTRACUR

36 0000

17

3401

08200641

060217

0110

3431

0421

1701

04053108

042503

19

3201

442401

3207

0401

0006

17

09020302

15

070201

022001

090520

2313

0211

0916

060605143801

2010

10

06042.9.

0613

081015

0607

Note: These correlations are resealed into the 100 to +100 interval for presematMn purposes. Thus. a reportedcorrelation of 40 represents a Pearson Product Moment Correlation of 0.40.The correlations were calculated for all nonmissing pairs of variables. The sample sizes for the individual ratingsvaried from 3.139 to 3.255.

Table 6.3. Results of the varimax rotation of the five-factor solution ofthe 14 perceptual ratings

Factors

Variable 1 2 3 4 5 Communality

DIVERSITY 0.501 0.644FACILITIES 0.639 0.490

GEOLOCATE 0.798 0.643REPUTATION 0.597 0.615LOWCOST 0.730 0.659SOCIALFIT 0.530 0.51

SPECPROG 0.641 0.461

COMMUNITY 0.761 0.608PREPGRAD 0.722 0.563AIDAVAIL 0.702 0.645CONTACT 0.725 0.581

ACADSTRN 0.692 0.488UGRADEMP 0.791 0.637EXTRACUR 0.823 0.697

Note: Only factor loadings with values of 0.50 or greater in absolute value are displayed in this table.

7468

tion for the five-factor solution are displayed inTable 6.3. These five factors, which account for58.9 percent of the variance in the original 14perceptual ratings, may be described as: aca-demic quality (ACADQUALITY), quality of per-sonal contact and "personalness" of the college(PERSONALNESS), nonacademic tifestyle consid-erations (LIFESTYLE), locational considerations(LOCATION), and financial considerations(MONEY). The five-factor solution communalitiesfor these 14 perceptaal ratings v /..aHee iangefrom 0.46 to 0.70. Thus, thk, five-factor solutionrepresents allout one-half to two-thirds of the var-iation in each of the 14 raw peceptual ratingsscale. We conclude that this reduced space rep-resentation of the 14 perceptual variables is in-terpretable and parsimonious, and that it cap-tures the essence of the original 14 rawperceptual ratings variables.

Construction of the composite perceptualratings indicesRather than use factor scores (as derived fromthe factor analysis results preniousl- described)directly as composite indices -3f college percep-tions. we const- d Alr own indices using theseresults froet alysis .: a guide. Inparticular, we (-,-.:ab i50-;4. the original scales in asimple weight.ecl rashion so that interpre-tation woik :ee faeizic:.1. The weights were theinverse of e. ted rating's standard de-viation, so :hat t;:e,6i,s; with more variabilitywould not fi:..tate the composite in-dices.

Our comp oete are defined as follows:

ACADQUALI w2FACILITIES + wtREPUIAl It) T + w7SPECPROG +PERSONALNr..: wilCONTACT w13UGRADEM;LIFESTYLE = wIDIVE:RSITY + w6SOCIALF4T - w"EXTRACURY.00ATION w3GEOLOCATE + w8COW-77 NITYMONEY = w5LOWCOST + wloAIDAVAIL

where the weights w1, w2 sci4 are the inverseof the perceptual rating standard deviations, ap-propriately resealed to sum to 1.0 in each of thesecomposite indices for ease of interpretation.These weights are displayed in Table 6.4.

A multinomial logit model ofcollege preference judgmentformationPreterence for a college is viewed as dependingon perceptual ratings, individual-institution in-teractions, and college-specific influences. In ourmodel of college choice behavior, preference re-fers to all things students value in a college exceptsituational constraints (including money consid-erations).

Model formulationUnconstrained preferences were obtained fromthe respondents to the mail survey. The studentswere asked to rank their three highest-preferencecolleges from among those to which they hadapplied. To unconstrain these preference judg-ments, they were specifically instructed to pre-sume that they had free choice among these col-legec (they were to assume that they hadadmissions offers from all colleges) and that costwas not an issue. These rank-ordered preferencesservei the dependent variable in the mdlti-noir .al logit model of preference judgment for-

he four nonmonetary composke perceptualratings indicesACADQUALITY, PERSONAL-NESS. LIFESTYLE, and LOCATIONfor each of

69 75

w9P1.;,EPGRAD + wi2ACADSTRN

Table 6.4. 3,Z.-7:,e. hts used in the development of the five composite percep-tual rat1.:/2:5

No. Variabl.:

Originalstandarddeviatkm

Inverse ofthe standarddeviation'

Resealedweight:42

1 DP/ ;TY 0.61 1.65 0.342 FA(...H.inEs 0.56 1.77 0.203 GEO LCC ATE 0.69 1.45 0.494 REPAATION 0.57 1.77 0.205 LOTLOST 0.64 1.56 0.486 FOC RLFIT 0.68 1.4.6 0.307 SPLZ-"ROG 0.59 1.69 0.198 ( ()WUNITY 0.68 1.48 0.519 PREK:RAD 0.50 1.99 0.22

10 Ai II WAIL 0.59 1.71 0.5211 C(XACT 0.68 1.47 0.4912 4.1: PSTRN 0.58 1.73 0.19

I Vdt.,DEMP 0.66 1.51 0.51i.XTRACUR 0.56 1.79 0.36

1. For e aci a, ng. ".r.v.tC of the standard deviation- equals one divided by the -original standard deviation.-2. Tt.r "resea...0 refer to the resealing of the inverses of the standard deviation so that the resealed

Eights . ;) indices add up to 1.0.

the (up to tir.:cf) college alternatives served as themain independent variables. In addition, college-Frpreific inr:icator variables were included foreach if he cAleges with more than 150 mentions

mail survey.T!iese base model variables are defined in Ta-

!-..ie 6.5. They all have straightforward interpre-tations, except perhapF for the variable MISSING.This variable is included to model out the effectsof missing raw perceptual ratings. As with allsurveys, there was some item nonresponse to theperceptual ratings questions. That is, some re-spondents provided perceptual ratings for somebut not all of the 12 nonmonetary perceptualratings. Methods of handling such missing datainclude deleting it from analysis, adding variable-Teethe missing-value indicator variables to ac-count for the influence of such values, or assign-ing a particular value to the missing variables

76

(such as the mean of the nonmissing values for avariable). Rather tl'an add an extra 12 such var-iables, or adopt the extreme option of droppingsuch preference sets from the analysis altogether,a single missing-value variable was added to themodel. MISSING equals the lumber of missingperceptual ratings values. Since the incidence ofmissing values was small, this single variableshould serve to conveniently account for theirinfluence.

Several other individual- institutlen interactionvariables were additional candidates forinclusion in our multinomial ! nodel of collegepreference judgment formation. Familial ties to acollege (whether either paren. Attended the col-lege) and distance from the campus to the stu-dent's residence were viewed as possibly beingrelevant (see Table 6.6 for definitions of theseextra variables). Since our prior beliefs of the

70

Table 6.5. Definitions of the variables included in the preference judg-ment formation modelGroup/variables Definition

Perceptual ratingsACADQUALITYPERSONALNESSLIFESTYLELOCATION

Co llege-spectfic effectsCOLLEGE1

COLLEGE2 throughCOLLEGE7

Other variablesMISSING

Academic quality index (a composite index)Personalness index (a composite index)Lifestyle index (a composite index)Location index (a composite index)

An indicator variable which equals 1 for the most frequently mentionedcollege in terms of applications submitted by our 1.549 mail survey respon-dents, and equals 0 otherwise.Indicator variables for the second through seventh most frequently men-tioned colleges in terms of applications submitted by our 1.549 mail surveyrespondents.

The number of missing original perceptual rating values (from 0 to 12).

Table 6.6. Other variables tested in the extended preference judgmentformation modelVariable Definition

FATHER

MOTHER

DISTANCE

An indicator variable that equals 1 if a student's father attended a college andequals 0 otherwise.An indicator variable that equals 1 if a student's mother attended a college andequals 0 otherwise.The distance (in 000s of miles) from the campus of a college to the residence of ast udent.

importance of these variables were less strongthan for those in the base model, they were ca-tegorized as being candidates for an extendedmodel. Specific hypothesis testing would indicatewhether they should be included in the modeL

Estimation and model-specificationanalysisA total of 1,224 students' data from the mail sur-vey were available for analysis. These studentshad applied to and had ranked at least two col-

leges, and they had provided the correspondingperceptual ratings data. Of these 1,224 students,1,181 provided sufficiently complete college rank-ing (with no ties) and perceptual ratings data topermit their use for estimation purposes.

Maximum-likelihood procedures were used toestimate the parameters (relative-importanceweights) of this multinomial logit modeL A linearadditive functional relationship was assumed.The results of this estimation are displayed inTable 6.7.

71

77

Table 6.7. Results of estimating the preference judgment formation model

Cot4ficir nt StandardVariable estimate Crfor T-Rati4o

ACADQUALITY 1.9869 0.1430 13.894PERSONALNESS 0.7148 0.0742 9.637LIFESTYLE 0.8138 0.1069 7.892LOCATION 0.7124 0.0752 9.479

MISSING 0.7189 0..3074 2.339COLLEGE1 1.2112 0.2004 6.046COLLEGE2 0.2582 0.2014 1.282COLLEGE3 0.9460 0.2270 4.167COLLEGE4 1.0334 0.2071 4.990COLLEGE5 1.2201 0.2333 5.230COLLEGE6 O. 7261 0.2413 3.010COLLEGE7 0.5790 0.2620 2.210

Summary statistUsNumber of choice sets = 1.181Initial = 1.181.1Final = 805.4Log-likdihood ratio index = 0.318

Note: Refer to the discussion in Appendix 1 for details and interpretati.ons of the various log-likelihood statistics.

Hypothesis tests were performed to assesswhether the variables described in Table 6.6should be included in our base model. With re-gard to the FATHER and MOTHER variables, therelevant chi-squared test-statistic value was 2.6(with the corresponding critical chi-squared valueof 9.2. for 2 degrees of freedom and a 1 percentlevel of significance). With regard to DISTANCE.the relevant chi-squared test statistic was 5.0(with the corresponding critical chi-squared valueof 6.6, for 1 degree of freedom and a 1 percentlevel of significance). In both cases, then, theresults suggest that these variables do not con-tribute significantly, given the presence of theother variables in the model. Thus, on thegrounds of parsimony. we chose not to includeFATHER, MOTHER, and DISTANCE in the pref-erence judgment formation model.

The results reported in Table 6.7 are for anexplosion depth of one. As in the case of thechoice model described in Chapter 4, only thefirst-choice prior preference data could be usedto estimate the preference model's parameters.Attempts to exploit the rank-ordered nature ofthe prior preference data, as described in Chap-man and Staelin (1982), were unsuccessful. Intesting whether the second prior preference rank-ing could be used, the cwiiclusion was that explo-sion to a depth of two was not appropriate for'hese data. The relevant chi-squared test-statisticvalue was 29.6 (with the corresponding criticalchi-squared value of 26.2, for 12 degrees of free-dom and a 1 percent level of significance). Thus,we reject the null hypothesis that the first-and second-ranked prior preference choice ob-servations yield equivalent relative-importance

7672

weights in this preference judgment formationmodel.

Interpretation of the preferencejudgment formation resultsAll variables (except one of the college-specificeffects) in our pieference judgment formationmodel are statistically significant at the 5 percentlevel, and most are statistically significant at wellbeyond the 1 percent level. The LLRI value of0.318 is toward the high end of :he range of LLRIvalues for comparable college choic: studies (seeTable A1.1 in Appendix 1 for LLRI values forother college choice studies. Of course, we aremodeling prior preference here, not final collegechoice). We conclude from this that our modelperforms well, in a statistical goodness-of-fitsense, in accounting for the determinants of pref-erence judgment formation.

In forming preferences, the most importantperceptual dimension is academic quality (ACAD-QUALITY). These results are consistent withother studies, such as Kohn, Manski, and Mundel(1976), Chapman (1977, 1979), Punj and Staelin(1978), and Manski and Wise (1983) where objec-tive measures of college quality were found to bethe most important determinant of college choice.

PERSONALNESS, LIFESTYLE, and LOCATIONare all important considerations to students whenthey form prior preference judgments about col-leges. In fact, their impact on prior preference isapproximately equal, with relative-importanceweights (coefficients) of 0.7148, 0.8438, and0.7124, respectively. Their influence on priorpreference is positive: holding other factors con-stant, increases in perceived PERSONALNESS,LIFESTYLE, and LOCATION improve the p iorpreference probabilities. However, the partial ef-fect of each of these variables individually is lessthan one-half of that of ACADQUALITY.

In interpreting the college-specific effects, it isimportant to note that they represent the incre-

mental impact of a college after accounting forthe perceptual ratings. Thus, if the perceptualratings had fully captured all the relevant dimen-sions, these indicator variables would not havebeen necessary. Six of the seven college-specificeffects are statiscically significant at the 5 percentlevel; all are positive. Holding other factors con-stant, being a top-seven college improves theprior preference probability by a positive amount,above and beyond that conferred by the percep-tual ratings indices.

MISSING is negative and significant (at a 5 per-cent level). Since it models out missing data onany of the underlying 12 perceptual ratingsscales, the negative sign is interpreted as missingdata being implicitly held against a college.

In responding to the mail questionnaire, stu-dents both provided ratings of colleges on theperceptual scales and reported their importanceweights for these factors (on a 1-to-4 scale). It isinstructive to compare our statistically inferredimportance weights (from the multinomial logitanalysis described above) with the self-reportedimportance weights for the factors as provideddirectly by the students. Some relevant summarystatistics for the self-reported importance weightsfrom the mail survey respondents are reported inTable 6.8. Four of the ACADQUALITY ratingsscales (FACILITIES, REPUTATION, PREPGRAD,and ACADSTRN) are among the five highest-ratedperceptual dimensions on a self-reported basis.Furthermore, if we construct average self-re-ported values for our composite indices (usingthe data from Table 6.8), the average self-re-ported weights are 3.32, 2.70, 3.09, and 2.72, forACADQUALITY, PERSONALNESS, LIFESTYLE,and LOCATION, respectively. This pattern and itsordering is virtually identical to the coefficientestimates reported in Table 6.6. However, notethat the coefficient estimate on ACADQUALITYfrom the multinomial logit model is more thantwice the size of the coefficient estimates on the

73 79

Table 6.8. Self-reported relative-importance weights ofperceptual dimensions

Perceptualdimension Definition

Summary statistics

MeanStandarddeviation

ACADSTRN Academic strength in area of interest 3.627 0.631REPUTATION Reputation 3.613 0.586DIVERSITY Academic diversity 3.332 0.743FACILITIES Facilities 3.321 0.718PREPGRAD Preparation for graduate study/career 3.216 0.841SOCIALFIT Social activities 3.122 0.821UGRADEMP Emphasis on undergraduate studies 3.017 0.831GEOLOCATE Location setting 2.919 0.913SPECPROG Special programs 2.842 0.912EXTRACIIR Extracurricular activities 2.809 0.876AIDAVAIL Financial aid availability 2.526 1.126COMMUNITY Community setting 2.522 0.909CONTACT Contact with admissions personnel 2.388 0.963LOWCOST Low cost 2.254 0.997

Note: Self-reported importance weights were reported on a 1-4 scale. where:4 = very important3 = important2 = somewhat important1 = not important.These self-reported importance weights are based on 1.549 responses to the mail survey.

three other composite perceptual indices. Theself-reported weights appear to understate thedifferences in importance across the factors.Nonetheless, this overall consistency betwee:.statistically derived relative-importance weightsand self-reported relative importance weights isnoteworthy. Such corroboration from two inde-pendent sources serves to reinforce the confi-dence that we may place in the multinomial logitmodel weights.

Individual differences analysisTo assess whether students' backgrounds influ-ence their preference weights, we conducted in-dividual differences analyses similar to those con-

ducted for the college choice model. Theseanalyses require the use of statistical-poolingtests to determine, for example, whether the rel-ative-importance weights of men are statisticallyidentical to those of women. The mechanics ofthese pooling tests for the multinomial logit modelare described in Appendix 1.

Demographic variables. We tested for hetero-geneity of weights for the following demographicvariables (and subgroups of students): averageSAT scores ("less than or equal to 675"; "morethan 675"), gender ("male"; "female"), plannededucational level ("bachelor's or uncertain";"graduate school"), planned major field of study("sciences"; "engineering"; "other"), and paren-

80 "

Table 6.9. Individual differences analysis: Pooling test results fordemographic variables'

- --Calculatedtest statistic

Degreesof freedom

Criticalvalue Conclusioo2

14.4 26.2k:erage SAT scores 12(2 groups)

Gender 15.6 12 26.2 ids(2 groups)

Planned educational level 11.6 12 26.2 n/s(2 groups)

Planned major field of study 52.6 Zi 43.0 Significant(3 groups)

Parental income 35.6 24 43.0 tl/s(3 groups)

1. A 1 percent level of statistical significance was used in these tests.2. Under **Conclusion:* --n/s- means that the calculated test-statistic value does not exceed the critical value. sothe null hypothesis that the groups have identical relative-importance weights cannot be rejected: -significant-means that the groups apparently are characterized by different relative-importance weights.

tal income level ("$30,000 or less"; "$30.001$49.999"; "$50.000 or more"). The results ofthese tests are displayed in Table 6.9.

The pooling test results shown in Table 6.9indicate that only in the case of major field ofstudy are the relative-importance weights differ-ent. Thus, we may conclude that the preferenceweights reported in Tabie 6.7 adequately describeall SAT levels (in the range represented in oursample. 550400), men and women, iAanned ed-ucation& levels (bachelor's only versus graduateschool intentions), and all income levels. Thereare no apparent individual ciifferences based onthese demographic variables. IIowever, sincethere are apparently some d;fferences arsoss ma-jor field of study groups, a detailed examinationof these differences is appropriate.

Major field of study effec: The coefficients forthe various major field of study groups are shownin Table 6.10. Major differences across fields ofstudy are described below.

The primary differences across fields of studyappear to be college-specific effects. The extraimpact of being specific top-seven colleges variessomewhat by the student's field of study. A sec-ond notable difference concerns the relativeweights on ACADQUALITY and LIFESTYLE. Inall field of study groups, ACADQUALITY is themost important consideration. However, LIFE-STYLE appears to be considerably more impor-tant to "other" students than it is to engineeringand science students. Indeed, while ACADQUAL-ITY is about three times as important as LIFE-STYLE for engineering and science students, it isonly about one and one-third times as importantas LIFESTYLE for "other" students.

In sum, individual differences exist for stu-dents classified by intended field of study, butthey appear to be relatively modest in scope. Per-ceived academic quality is consistently the mostimportant consideration for students in all fieldsof stuJy.

75..

31

Table 6.10. Coefficient estimates for different planned major fields of studyAll studentswith reportedmajor field

Variable of study

ACADQUALITYPERSONALNESSLIFESTYLELOCATION

MISSINGCOLLEGE!COLLEGE2COLLEGE3COLLEGE4COLLEGESCOLLEGE6COLLEGE7

Summary statisticsNo. of choice setsInitial LLFinal LLLLRI

Students repmiing that

Engineering

their major field of

Science

-tudv NOuld be:

"Other-

1.9781** 2.2985** 2.1949** 1.6911**0.7159** 0.7787** 0.7168** 0.7683**0.8305** 0.6603** 0.7343** 1.2763**0.7066** 0.5516** 0.8808** 0.6274**

-0.7145* 0.2080 -1.1325* -0.48001.2107** -2.1885 1.7027** 0.9526**0.2456 0.4574 0.3150 0.10690.9214** 1.0030 1.5198** 0.48741.0332** 0.8044* 0.8870** 1.7041**1.2438** 1.3137** 1.3291** -1.21400.6924** 1.4574 0.5289 0.8207*0.5774* 0.3424 1.0919** 0.1902

1161 278 492 391

-1170.5 -280.7 -498.7 -391.0-798.9 -169.7 -331.6 -268.3

0.317 0.395 0.329 0.314

Note: Refer to th e. discus.sion in Appendix 1 for details and interpretatimis of the variote., log-likelihood statistics.Significane e. at the re- 15%1 level is denoted by "*"'" 1"*-1 tone-tailed test).

SummaryThese high-ability students seem quite rational intheir college preferences: a college's perceivedacademic quality in the student's area of interestis of paramount importance. However, the stu-dents also give weight to perceptions of lifestyle.location, and quality of personal contact associ-ated with a college. For colleges, these resultssuggest that academic and nonacademic lifestyleconcerns are both of interest and concern to high-ability students. Colleges student recruitment ef-forts should be directed in the first instance tothe academic component of the college-going ex-perience, but c:her aspects should definitely notbe overlooked.

The general complexity of the college prefer-ence judgment formation process is noteworthy.All four composite perceptual ratings indices plusmost of the college-specific effects are statisti-cally significant. As with the college choice pro-cess, many factors are implicitly weighed bythese high-ability students when they form pref-erence judgments about colleges.

82 76

7. Antecedents of college choicebehavior: Perception judgmentformation

In this chapter, we seek to analyze the determi-nants of perceptions. The preference judgmentformation process modeled in Chapter 6 indicatedthat four composite perceptual indices were im-portant determinants of prior preference. We nowwish to attempt to explain how objective collegecharacteristics influence students' perceptions ofcolleges.

A major omitted variable problem arises in thisperception formation judgment modeling effort.In our multistage college choice model, describedin Chapter 2, we postulated that perceptions de-pend on both college characteristics and on theinformation environment. Since our focus in thisstudy was on choice behavior, we made no effortto measure relevant aspects of the informationenvironment possessed by each student.

The perception judgment formation modelingstage involves using composite ratings of percep-tions and of colleges' attributes, both of whichare needed to simplify the modeling task. Thecomposite perception indices were developed inChapter 6. The construction of composite collegecharacteristics indices is described in the follow-ing section, prior to presenting and discussing thestudy's findings with regard to the determinantsof perception judgment formation.

ConstrucC,on of composite collegechara.".-1-i...NiLs indicesPrior to L:---cos,,ing the results of the perceptionformation 'cletteling effort, it is necessary to de-scribe some initial efforts at data reduction forthe independent variables in the perception for-mation model. With regard to college character-istics, these efforts concerned constructing com-posite indices of academic quality, location, andnonacademic activities.

As & scribed in Chapter 2, three major forcesare presumed to influence a student's perceptionof a college: the actual objectively verifiable at-tributes which characterize a college, individualinstitution interactions, and the information pos-sessed by the student about the college. In thisstudy, we did not measure the information envi-ronment associated with the college choice deci-sion, since most of this information is presumablydeveloped in the context of the search process.

Our primary source of objective variables todescribe the colleges was the College Board'sAnnual Survey of Colleges (ASC). Among the in-dividualinstitution variables of interest are pa-rental ties and distance (from the student's hometo a college's campus). College-specific "brandname" effects may also be present. The completelist of independent variables included in our per-ception formation model is described in Table7.1.

The objective college characteristics that are

83

Table 7.1. Definitions of the variables included in the perception judg-ment formation model

Group/variable Definition

Academic characterAQSCORENUMMAJOR

Institutional characterMEN%COEDNESS

PRIVATE

UG%

Lifestyle aspectsACTSCORELOCSCORE

IndividualinstitutioninteractionsFATHER

MOTHER

DISTANCE

College-specific effectsCOLLEGE1

COLLEGE2 throughCOLLEGE7

Academic Quaiity Score (a composite index)Number of majors available

Percentage of all undergrafl .ates who are maleThe degree of "coedness J:t a campus. This is dcfinul to be:

100-MEN% if MEN%>50;60 if MEN% = 50;MEN% if MEN%<50.

An indicator variable which equals 1 if a college is private, and 0 other-wise.Percentage of all students who are undergraduates.

Activity Score (a composite index).Location Score (a composite index).

An indicator variable that equals 1 if a student'sand equals 0 otherwise.An indicator variable that equals 1 if a student'slege, and equals 0 otherwise.The distance (in 000s of miles) from the campusdence a student.

father attcnded a college,

mother attended a col-

of a college to the resi-

An indicator variable that equals 1 for the most frequently mentioned col-lege in terms of applications submitted by our 1,549 mail survey respon-dents, and equals 0 otherwise.Indicator variables for the second through seventh most frequently men-tioned colleges in terms of applications submitted by our 1,549 mail surveyrespondents.

presumed to influence students' perceptions fallinto three board categories: academic character,institutional character, and lifestyle aspects.

Academic characterWith regard to academic character, a compositeindex was constructed to describe a college's ac-

ademic quality, reputation, and prestige. This in-dex includes a number of variables that measurestudent input quality, resource base, and otherquality-related measures. The resulting academicquality composite index, AQSCORE, does not relyon a single measure of quality, but rather at-tempts to include a range of related indicators of

84 78

academic quality. in addition, this index of eightdifferent variables overcomes some missing-dataproblems that were present in the ASC data. Theeight variables included in this index are definedand described in Table 7.2. A principal compo-nents factor analysis served to identify these var-iables. AQSCORE is the arithmetic mean of theavailable adjusted academic quality variables fora college, where the adjusted variables have beentransformed to standard deviate form (mean ofzero and standard deviation of one) so that theirunits are comparable. Missing values for a vari-able were ignored in this calculation.

In constructing the academic quality index, 27colleges with 10 or more mentions in the mailsurvey had missing SAT data in the ASC data set.Supplementary data sources used to estimate theSAT scores of these colleges were taken fromFiske (1982), McClintock (1982), and Barron's

Profiles of American Colleges (1980). Where thesesecondary sources yielded multiple SAT scores,averages were used.

A second academic character variable is num-ber of majors offered, NUMMAJOR. This variablecaptures both the breadth of the available aca-demic offerings and the size of the educationalinstitution.

Institutional characterUnder the heading "institutional character," fourvariables are included: MEN%, the percentage ofthe students who are male; COEDNESS, a mea-sure of how coeducational an institution is; PRI-VATE, an indicator variable for whether a collegeis private; and UG%, the percentage of all stu-dents who are undergraduates. COEDNESS is anindex that takes on the value 50 for a collegewhere the male/female ratio is 1:1 and takes on

Table 7.2. Variables used in the academic quality index

Variable Definition

Summary statistics

Mean S.D.

SAT Mean SAT scores of matriculants 527.6 60.6 372SFRATIO Studentfaculty ratio 19.5 10.5 468FACPHD% Percentage of faculty with Ph.D. degrees 67.2 21.1 383ADMIT% Admission acceptance % (percentage of

applicants who are admitted)70.4 18.8 494

YIELD% Yield rate % (percentage of admitted ap-plicants who matriculate to a college)

51.8 16.2 487

FC1YR% Percentage of freshmen who successfullycomplete their first year

86.5 9.0 512

FR2YR% Percentage of freshmen who return forsecond year

79.9 11.3 473

GRAD% Percentage of graduating students who goon for graduate studies

37.9 19.1 365

Note: These variables describe the 550 colleges to which students reported they applied one or more times in themail survey responses. ln forming the academic quality index. AQSCORE. these eight variables (in standard deviateform) were combined additively, except for the variables SFRATIO and ADM1T%, which were subtracted from thecomposite index. These subtractions occurred for these specific variables because they are of the "less is bette-"variety, while for all other variables "more is better."

79 85

values approaching zero as that ratio departs from1:1 in either direction.

Lifestyle aspectsTwo specific lifestyle aspects are included: therange of nonacademic activities offered, ACT-

SCORE. and a variable measuring location. LOC-SCORE.ACTSCORE is the sum of the number of the

following activities available at a college: sports.performing arts. clubs special programs and ser-vices for students, and special remedial pro-grams. Thus, this variable is designed to capturea range of nonacademic activities supported by acollege and to which a student would have accessshould he or she choose to attend.LOCSCORE is a composite index constructed

from three separate location variables availablein the ASC data file. These three variables referto the population of the nearest city/town and twoother campus environment measures related tourbanness. These three raw variables were trans-formed to standard-deviate form and then aver-aged to develop the LOCSCORE composite indexof location. Higher (lower) values of 1DCSCOREdenote more urban (rural) campus locations.

Individualinstitution interactionsParental ties to a college and distance are in-cluded in the perception-regression models tocapture the potential influence of these relevantindividualinstitution interactions. Parental tiesto a college may positively impact perceptions .partially due to the increased access to informa-tion about the college offered by this personalconnection and partially due to students' valuesand views being influenced by their parents. Dis-tance ma-; be negatively related to perceptions,due to the difficulty associated with learningabout distant colleges. Such difficulty may in-crease a student's uncertainty about a college,resulting in less favorable views being reported.

College-spectfic effectsCollege specific indicator variables for the sevencolleges with 150 or more mentions by studentsin the mail survey were also included in the per-ception formation models. These variables mea-sure the influence of the college's brand name--above and beyond that which is reflected in theperceptual rating scores.

Functional form of the perceptualformation modelSince the perceptual ratings have been standard-ized to reflect relative perceptions. the indepen-dent variables must also be expressed in relativeterms. The actual form of the perceptual forma-tion models estimated was as follows:

R'scd Rcr.i = b (Z, Zr.)

where

a st udenta college (and r* represents a college other thancollege r)a standardized composite perceptual score forpemeptual dimension d Of college c fOr student

the vector of independent variables in the ver-ceptual formation model for college c.

In this equationh b is a vector of parameters (rel-ative importance weights) to be estimated.

In estimating the model in the equation. onecollege alternative is "lost" for each student 'aythe relativeness transformation. Only the uniquenumber of college comparisons matters, not !henumber of colleges. Thus, a student with threecolleges rated yields two unique comparisons(college 1 versus college 2, and college 1 versuscollege 3). Similarly, a student who rated twocolleges provides just a single unique comparison(college 1 versus college 2).

Note also that the model does not contain a

8 6 80

constant term, since the variables and the modelare all express,d in relative terms.

Results of estimating theperception formation modelSeparate rew !ssior models were estimated foreach of the feu: : ,inposite perceptual measures.All the independent variables described in Table

7.1 were included in each of these perceptual-regression models. Table 7.3 contains a summaryof the results of these regression estimates. De-tailed results may be found in Tables 7.4 to 7.7.

As may be noted, the goodness-of-fit of thesemodels range from an R2 of 0.076 for the LOCA-TION perception equation to an R2 of 0.298 forthe PERSONALNESS equation. These relativelylow levels of goodness-of-fit are, however, not un-

Table 7.3. Summrzry results of ectimating the perception formation model

Independentvariabks

Composite indices of the perceptual ratings (dependent variables)

LOC.A.TIONACADQUALITY PERSONALNESS LIFESTYLE

AQSCORE + + [1] + + [1]NUMMAJ OR [3] + + [2]MEN% + + [4]COEDNESS + + + [2]PRIVATE + + [1]UG% [2] + + + + [4]ACTSCORE + + [3]LOCSCGRE [4]FATI1ERMOTHERDISTANCE + + [3]COLLEGE! + + [3] [2]COLLEGE2 + + [5]COLLEGE3 + + [5] [1]COLLF GE4 + + [5]COLLEGE5COLLEGE6 + +COLLEGE7 + + [4] [5]R2 0.264 0.298 0.129 0.076Number of

observations2.021 2.016 2,021 2.021

The coding in this table is as follows (all are one-tailed tests of significance):" + +" = a coefficient is significantly positive at the 0.01 level

"+ = a coefficient is significantly positive at the 0.05 level"" = a coefficient is significantly negative at the 0.05 level

" " = a coefficient is significantly negative at the 0.01 level.The five most important variables in each regression equation. as measured by the standardized regression coeffi-cients, are indicated by [1], [2], [3], [4], and [5]. Detailed regression results are reported in Tables 7.4 to 7.7.

Table 7.4. Results of estimating theperception formation model:ACADQUALITY1

Coe" ient StandardVariable2 estiil error T-Ratio

AQSCORE 0.0168 10.658NUMMAJOR -0.001:- 0.0047 -0.319MEN% 0.0031'; 0.0009 3.845COEDNESS -0.0041 1.0011 -3.688PRIVATE 0.0403 1.346UG% -0.0075 0....:.../ 8.411

ACTSCORE 0.0018 0.0. :7 1.042T 'ICSCORE 0.0267 0.0139 L917

0.0099 C.2310.0967 0.0..

DIS 0.0123 0.C1 0.77COLW 0.3143 0.054COLLEG 0.2161 4.882COLLEC-,:. 0.0521 0.5i2.1 O.C87

COLLEGi. 0.0829 0.0334COLLEG3 0.0966 0.0518 L864COLLEGL6 0.1482 0.0540 2.71?COLLEGE' 0 2927 0.0599 .285

Summary statisticsR2 = 0.264Number of observations = 2,021

1. A linear-in-parameters functional form with additive dis-turbance terms was assumed. Estimation was via thdinaryLeast Squares.2. See Table 7.2 for definitii.:-s of these variables.

expected. Recall that a key component of per-centions-he information environment-is notincluded in our regression equations. This otols-sion ,..edues our ability to explain more of thevariance in the composite rerception rating in-dices. Also, our objectively verifiable variablesare strictly quantitative in nature. They do no;measure intangib lo. quality dimensions well, if atall. 1Tc: example, our rnea-Aure of extracurric&aractivities, ACTSCORE, is a simple count or theavailable extracurricular activities. Quality con-

Table 7.5. Results of estimating theperception formation model:PERSONALNESS1

Coeffirient StandardVariable2 estimate error T-Ratio

AQSCORE 0.0293 0.0244 1.203

NUMMAJOR 0.0439 0.0068 -6.494MEN% 0.0029 0.0013 2.202COEDNESS 0.0006 0.0016 0.389PRIVATE 0.5887 0.0434 13.567UG% 0.0045 0.001.3 3.438

ACTSCORE 0.0064 0.0025 2.603LOCSCORE 0.1105 0.0202 5.4.64

FATHER 0. 0970 0.0574 1.690MOTHER 0.1015 0.0769 -1.320DISTANCE 0.0990 0.0229 4.355

COLLEGE1 -0.7396 0.0790 -9.361COLLEGE2 0 A1056 0.0642 0.088COLLEGE3 0.0390 0.0766 0.509COLLECE4 -0.3041 0.0731 4.161COLLEGES -0.0911 0.0751 1.212

COLLEGEL .0041 0.0783 0.052COLLEGE7 0.3943 0.0869 -4.539

Summary statisticsR2 = 0.298Number of observations = 2.016

1. A linear-ir,paratneters functional form with additive dis-turbance tdrms was assumed. Estimatiim was via OrdinaryLeast Squai.-.s.2. See Table 7.2 for definitions of these variables.

siderations ,sociated with such activities are un-measured

Academic quality perception formationThe resul = in Tables 7.3 and 7.4 indicate thatour high-abil.r,.. students' perceptions of collegeacademic quail:, are primarily rekted to the fol-lowing college charActeristics:

A college's actual academic quality (the higher,the better);

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Table 7.6. Results of estimating theperception fermation model:LIFESTYLE1

Variable2C(efficientestimate.

Standarderror T-Ratio

AQSCORE 0.0932 0.0198 4.710T`TUMMAJOR 0.0253 0.0055 4.621

MEN% -0.0035 0.0011 -3.252COEDNESS 0.0029 0.0013 2.202PRIVATE -0.0088 0.0352 -0.249UG% 0.0041 0.0011 3.814ACTSCOPE 0.0080 0.0020 3.996LCK:SCORE 0.0307 0.0164 1.869

FATHER 0.0712 0.0466 1.529MOTHER 0.0083 0.0624 0.133DISTANCE 0.0282 0.1862 1.516

COLLEGE1 0.0141 0.0641 0.221COLLEGE2 -0.0117 0.0521 0.225COLLEGE3 0.2210 0.0621 3.556COLLEGE4 0.1158 0.0593 1.969COLLEGES -0.0790 0.0610 -1.305COLLEGE6 0.1490 0.0636 2.344COLLEGE7 0.09,0 0.0705 1.347

Summary a; atistics= 0.129

Number of obser,ations = 2.021

1. A linear-in-para:lie ,ers -.3I form with additive dis-turbance terms wa, assumed. Estimatior was via OrdinaryLeast Squar:s.2. See Table fOr definitions of these variables.

A college's undergra+)ate concentration tenesmaller the undeigracka;<_: student compositionin the total studeid body, tile better; the g:::!aterthe graduate student comi;osition, the better);and

A college's gender r : Are greater the concen-tration of well, the o:In addition, 111,.!re are some college-specific ef-fects in operation here.

Actual academic qvality, as proxied by ourcomposite index AQSCORE, is 1111.. 'Pri mary deter-

Table 7.7 Results of estimating theperception formation modd:LOCATION1

Coefficient StandardVariable= estimate error T-Rwio

AQSCORE 0.0097 0.0277 0.352NUMMAJOR -0.0282 0.0077 -3.678MEN% -0.0056 0.0015 -3.793COEDNESS 0.0070 0.0018 3.817PRIVATE -0.0304 0.0492 -0.618UG% -0.0009 0.0015 -0.592ACTSr.ORE 0.0003 0.0028 0.110LOCSCORE 0.0114 0.0230 0.495FATHE R 0.0811 0.0651 1.245M 9THER 0.0740 0.0872 0.849DE-.TANCE -0.0993 0.0260 -3.804COLLEGE1 0.2042 0.0897 2.277COLLEGE2 0.029 0.0728 0.403COLLE:;E3 -0.5239 0.0869 -6.029COL LEGE 4 3.3108 0.020 3.747COLLEGES 0.2103 0.0853 2.466COLLEGE6 -0,2312 0.0889 -2.601COLLEGE7 -0.0453 0.0936 -0.464

Summary swisticsR2 = 0.076Number of observations 2.021

1. A linear-in-parameters functional form with additive dis-turbance terms was assumed. Estinwion was via OrdinaryLeast Squares.2. See Titi.li 7.2 for definitions of these variables.

minant of perceived aca,!emic quality. In addi-tion, colleges with well-recognized academiequality also tend tc have substantial numbers ofgraduate students !n their student bodies. Thus,the role of UG% is not unexpected.

It i lso significant that ACTSCORE and LOC-SCOhE are not determinants of academic qualityperception. ACTSCORE and LOCSCORE have noparticular theoretical relationship to academicquality, so zheir irrelevance is of note in judgingthe performance of this regression model. Our

89

empirical results are consistent with this a prioritheory.

Personalness perception formationThe results in Tables 7.3 and 7.5 indicate thatour high-ability students' perceptions of college"personalness- are primarily related to the fol-lowing characteristics:

Whether a college is private ("privateness- ispositively perceived);

A college's breadth of course offerings, as prox-ied by number of majors (the more majorsacorrelate of college sizethe less perceived "per-sonalness"):

A college's location (more "ruralness- is viewedpositively);

Distance from a student's home to a college'scampus (more distant colleges are viewed asbeing more "personal"); and

A college's undergraduate concentration (themore the college's student body is concentratedin undergraduate students, the better).There are also some college-specific effects inevidence.

Small, private colleges are perceived to be es-pecially personal. Recall that the number of ma-jors (NUMMAJOR) and breadth of extracurricularactivities (ACTSCORE) are correlates of collegesize. Thus, larger public colleges are, in general,viewed as being less "personal." Such collegestend to be in urban areas; small private collegesare often in rural areas. Thus, the negative LOC-SCORE effect is consistent with these other re-sults.

A priori theoretical considerations would sug-gest that college quality should have no influenceon perceived "personalness." The evidence isconsistent with such a view, since AQSCORE isnot significantly related to PERSONALNESS.

Lifestyle perception formationThe results in Tables 7.3 and 7.6 indicate thatour high-ability students' perceptions of college

lifestyle are primarily related to the followingcharacteristics:

A college's academic quality (the higher the bet-ter);

The size of a college, as proxied by number ofmajors and breadth of available extracurricularactivities (the more the better):

The college's undergraduate concentration (thehigher the be:ter);

Degree of "coedness- (a balanced enrollmentsplit between men and women being preferred).Several college-specific effect,. are in evidence.

The results are in accord with a priori expec-tations. Larger colleges are., in general, pre-ferred. This is sensible since larger schools offermore and varied living, nonacademic, athletic,and extracurricular opportunities. However, AQ-SCORE is the primary determinant of perceivedlifestyle. Thus, colleges with high qualityandthe associated concentration on academic aspectsof the educational experiencealso are viewedas being desirable from a lifestyle perceptionviewpoint. These findings suggest that both aca-demic and nonacademic considerations are re-flected in our students' perceptions of litestyle.

Location perception formationOur model for LOCATION has relatively poor sta-tistical performance, compared to the ot' r threecomposite indices. Thus, these findings shouldbe taken as tentative.

The results in Table 7.3 and 7.7 indicate thatour high-ability students' perceptions of collegelocation are primarily related to the followingcharacteristics:

College gender mix (single-sex institutions areviewed negatively);

Distance (colleges farther away from a student'sresidence are viewed negatively);

College size, as proxied by numbers of majors(larger colleges are viewed less favorably).Strong college-specific effects are in evidence:

90

Five of the seven collt.ge-specific effects ar sta-tistically significant.

An ideal l, ition for a college is close to astudent's home, in a nonurban setting (sincelarger collet_ s tend to lp,! located in urban cen-ters). and with a nk .y balanced coed studentpopulation.

ConclusionsEven with a relatively low level of statistical fit.our perception judgment formation equationsdemonstrate interpretable and significant link-ages between objectively verifiable college char-acteristics and perception ratings indices. Theresults are. in general, quite consistent with apriori expectations. Research more centrally fo-cused than this study on the determinants of stu-dents' college perceptions could examine a largerarray of college attributes, students' levels of in-formation about colleges, and possible individualdifferences among students in the factors influ-encing perception judgment formation. The morelimited analysis reported here suggests that suchresearch efforts would meet with reasonable suc-cess in demonstrating interpretable linkages be-tween college characteristics and student percep-tions.

It is interesting that many factors (statisticallysignificant variables) appear to be at work in in-fluencing the formation of college perceptionjudgments for our high-ability students. As withour findings about the determinants of collegechoice behavio; and preference judgment for-mation, many cons.derations are at work withregard to the d. Lrminants of perceptions.

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8. Other factors influencingcollege choice behavior:Campus visitsand post-admissions contacts

In this chapter, we focus on two other factorswhich may influence college choice behavior:campus visits and post-admissions contacts.Here, we study the role, incidence, and influencethat such visits and contacts exert on collegechoice behavior.

Our interest in post-admissions contacts isbased on several considerations. First, such con-tacts are between a college and its admitted ap-plicants. Thus, they involve genuinely interestedstudents which the college has already identifiedas being academically acceptable. Second, thesecontacts may be managed and influenced to someextent by colleges if it's worthwhile to invest re-sources, time, and effort in so doing.

For campus visits, we may assume that stu-dents visit only colleges in which they have con-siderable interest. Thus, the act of visiting is animportant signal to the college of the student'sinterest. If the act of visiting a college's campusis a good signal as to a student's ultimate enroll-ment choices, then once again colleges mightwish to attempt to manage this process with care.

Direct mail appears to have assumed the roleas the primary student recruitment marketing

I in college admissions. However, direct mailis efficient (inexpensive) but not effective on aper-student-contacted basis. Other things (highschool visits, participation in college fairs/nights,campus visits, and post-admissions contacts) aremore personal and are likely to be more effectivebut not as efficient (more costly) on a per-student-contacted basis. The key issue concerns the rel-ative degrees of effectiveness and efficiency ofalternative recruiting tools. In studying variousforms of post-admissions contacts, we wish toaddress the effectiveness issue directly.

Some methodological issuesOur study is of the cross-sectional. variety. It isnot experimental in nature. This raises some im-portant issues with regard to assessing the roleand influence of campus visits and post-admis-sions contacts on college choice behavior. Thecrux of the issue concerns causality assessmentand direction of causality.

If we observe a high correlation between cam-pus visits or post-admissions contacts and choicebehavior, we still may not be able to classify sucha factor as being causally related to behavior. Theproblem is that we did not know the student'sdegree of interest prior to the visit or contact.

In our surveying, we asked students to identifythe nature of any post-admissions contacts withthe colleges to which they were admitted and also

92 86

to identify the colleges (if any) that they had vis-ited. We did not ask them who initiated the con-tact, nor did we ask when the campus visit oc-curred.

Thus, the causality-assessment problem re-lates to the following types of issues: Did a stu-dent initiate a contact because he or she wasparticularly interested in a college, or did thecontact increase the student's prior interest? Dida student visit a campus because he or she wasalready highly interested in the college, or did thecampus visit spark the student's high interest?Probably both kinds of influence occur, but itwould be a serious mistake to assume that thedirection of causality flows only from the contactto the interest.

In conclusion, then, our empirical resultsshould be taken only as suggestive of patterns,and not as definitive findings. Still, they representa large-scale effort to examine this aspect of col-lege choice behavior.

Empirical results:Four key numbersFour key numbers should be noted as we turnour attention to the empirical results:

Number of students who replied to the tele- = 1.183phone surveyNumber of admissions offers = 3.988Mean number of colleges to which these = 3.4students were admittedProbability of choosing any college (given = 29.4%that it was in a student's choice set andthat the student was admitted to the col-lege)

Each of the 3,988 offers to the 1,183 studentshad, on average, a 29.4 percent chance of beingselected (1183/3988 expressed in percentageterms). These numbers represent base-line re-

sults with which other figures and results will becompared.

Empirical results: Campus visitsTo learn about various college options. studentsmay consult a variety of sources. An actual visitto the campus of a college is a particularly notablesource of information. It provides an opportunityfor a student (and his parents) to view the livingenvironment and meet with a number of relevantpeople (faculty, other college officials, and otherstudents).

A feature of our campus visit data should benoted. These data do not include information onwhen the visit actually occurred. Thus, a campusvisit might have occurred during the early searchphase of the college selection process or it mighthave been a true post-admissions contact, occur-ring after the student had been notified of beingadmitted.

Our high-ability students engaged in a substan-tial amount of college campus visit activity: 91.7percent (1,085 of 1,183) of our respondents madeat least one campus visit and 64.5 percent of all3,988 admissions involved such a visit. Our sur-vey respondents reported that their opinions ofcolleges generally improved as a result of campusvisits. Indeed, 52.6 percent of campus visits ledto a student reporting a more positive view of thecollege, while in only 9.9 percent of the visits didthe student report that the experience ultimatelyresulted in a more negative view of the college.Our respondents reported no change in theirviews of colleges for 37.5 percent of the visits.

Table 8.1 contains some information on visitingpatterns and actual choices. Knowing nothingabout a student's campus visit activities or col-lege preferences, an average choice set size of3.4 colleges implies that each college has, onaverage, about a 29.4 percent chance of beingchosen. However, as the data in Table 8.1 indi-

87.- 93

Table 8.1. Correlation of campusvisits and college choices

Frequencydalow.-

ing a tAlege (%)

Given acampusvisit

Given nocampusvisit

All students 39.7 12.6Stude its making 1 visit only 82.5 19.2Students making at least 1

visit43.3 9.9

Studunts making at least 2visits

28.9 6.5

Note: Base for "all students"Base for "1 visit only"Base for "at least 1 visit"Base for "at least 2 visits"

= 1.183 students= 291 students= 1.085 students= 794 students.

cate, knowing something about campus visit ac-tivities can considerably change these base-linefigures. Across all students and campus visit fre-quencies, if we know that a student has visited acampus, then we can revise our 29.4 percentchoice-probability figure to 39.7 percent for sucha visited college. Furthermore, 82.5 percent ofstudents visiting only one campus ultimately en-roll at that college.

Our data support the conclusion that studentswho viit a college tend to choose the visitedcollege. The strength of our findings almost sug-gests that there may be an empirical "law ofcampus visits": "Students who visit tend tochoose the visited college." This is no doubt be-cause a visit is a sign that a student has a highdegree of interest in a college.

There are a variety of implications to collegesthat flow from this finding. First, colleges shouldfind it worthwhile to devote considerable atten-tion to managing the campus visit process. Acampus visit is not a minor matter in the mindsand behavior of students. Second, they should tryto encourage applicants, prospective applicants,

and admitted applicants to visit their campuses.Third. colleges should attempt to make it easy(and as low-cost as possible) for students to makecampus visits. Note that here. "cost" is used inthe senses of monetary. time, and "red tape"considerations.

Empirical results:Post-admissions contactsBy definition, post-admissions contacts occur af-ter admissions decisions are communicated tostudents, but before students actually choose acollege. Such contacts are especially interestingbecause they take place so close to the actualpoint at which the college choice decision occurs.

"rii data in Tables 8.2, 8.3, and 8.4 suggestthat post-admissions contacts are infrequent, butapparently almim always positive. Only 52.2 per-cent of all admissions involved some such contact(with one or more contacts with one or more col-leges). Th e. corresponding figures for contact bymail, telephone, and meeting are 37.4, 21.9, and19.4 percent, respectively.

The incidence of post-admissions contacts by

Table 8.2. Frequency of paq-admissionscontacts1

No. ofcontacts

Contactby anymeans(overall)

Contactby

letter

Contactbytelephone

Contactbymeeting

0 47 8% 62.6% 78.1% 80.6%1 23.0 2. 19.1 11.32 14.6 9.4 2.5 5.83 7.0 2.5 .3 1.64 3.8 .6 .0 .65 + 3.8 .4 .0 .2

100.0% 100.0% 100.0% 100 0%2

1. These data reflect the responses of 1.183 students.2. Due t,) rounding, some totals do not add to 100.0%.

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Table 8.3. Incidence of varioustypes of post-admissions contacts

Contact incidence (%)_Coatact with Letter Telephone Mectutg

Dean/President 3.6 .3 1.3Faculty member 15.8 3.4 9.5Coach 3.5 2.1 1.1Other students 4.1 4.8 4.4Alumni 9.0 8.8 5.3Admissions personnel 12.6 4.0 6.4Honors program 2.4 .5 1.4Other 4.2 1.2 1.6

Note: These data reflect the respt,nses of 1.183 students.

various means (letter, telephone, and meeting) bydifferent types of people affiliated with a collegeare displayed in Table 8.3. Contact by letter ismost often by a faculty member (about 15.8 per-cent of all students teported one or more contactsby letter from a faculty member), with admissionspersonnel running a close second in frequency ofcontact. Alurn:ii are most frequently associated

with telephone post-admissions contacts. For per-sonal meetings, the three most frequent post-ad-missions contacts are with faculty members, ad-missions personnel, and alumni.

The results in Table 8.4 suggest that the morepersonal the contact, the greater the chance thatit will have a positive impact on the student.Contact by letter results in particularly positiveinfluences on the students in 26.7-40.2 percentof the r mtact occasions, across the v,rious typesof contact people. The corresponding results fortelephone and meeting contacts are 30.4-50.0percent and 47.3-66.0 percent, respectively.Stated another way, the typical post-admissionscontact by letter results in no particular influenceon the student; however, the typical contact inperson during a meeting results in a positiveimpression being left with the student.

The data in Table 8.4 also suggest that sharpdifferences among the "contact" persons do notseem to exist. For example, for contact by letter,the most positive reported contact was with hon-ors programs, where 40.2 percent of these con-tacts were reported as positive; and the least pos-itive reported contact was with alumni, where

Table 8.4. Reported influence of various types of post-admissions contactsReported effect of a contact (9k'). given that a contact occurred

...:ontact with

Letter Telephone Meeting

Positive Negative Positive Negative Positive Negative

Dean/President 34.5 .0 50.0 .0 66.0 4.0Faculty mer iber 29.4 .6 44.5 1.5 59.7 4.2Coach 28.9 .7 42.2 1.2 59.5 2.4Other students 34.0 2.4 37.3 .5 57.1 6.2Alumni 26.7 .6 31.9 .9 58.7 4.2Admissions personns4 28.1 .8 42.8 1.9 53.1 5.9Honors program 40.2 1.0 50.0 5.0 47.3 9.1Other 28.0 2.4 30.4 6.5 51.6 9.7

Note: These riata reflect the responses of 1.183 students. The neutral responses are not shown. since: positiveneutral + negative 100.0%.

89 9 5

26.7 percent of these contacts were reported aspositive. The "positives" for honors programsversus alumni letter contacts is only in the ratioof 1.5:1. Thus, there is not really that much dif-ference across the various types of contacts. Itappears that, for post-admissions contacts. "acontact is a contact is a contact."

Given these findings, it is puzzling that post-adm:ssions contacts occur so infrequently. Ofcourse, costbenefit considerations are relevanthere, as are logistical considerations. The timebetween admissions decision and reply date maybe too tight for large-scale post-admissions con-tact efforts. But, what about selective contactefforts directed toward specific students or typesof students? The thoughtful management of po:t-admissions contacts appears to be a worthwhileendeavor for a college.

Concluding remarksThe true effect of campus visits and post-admis-sions contacts on choice is uncertain. For campusvisits, we don't know the student's pre- and post-visit levels of interest; for post-admissions con-tacts, we don't know who initiated the contact.Still, these results are suggestive of some impor-tant patterns. Further research, with pre- andpost-measures of a student's interest in a collegebefore and after the contact, is needed to clarifythe role and influence of campus visits and post-admissions contacts on college choice.

9 690

9. Changes in college choice afterthe initial decision

College admissions officers have, in recent years.reported increasing numbers of "no-shows---students who simultaneously accept admissionsoffers and submit deposits to hold places at mul-tiple colleges, deferring decisions concerning thecolleges in which they will actually enroll. Be-cause of this phenomenon, the college choicesreported to us by students in the telephone follow-up interviews might potentially differ from finalenrollment choices for a sizable number of stu-dents. Apart from students changing their collegechoices, others might decide not to attend anycollege in the fall. If changes in college plansoccurring over the summer months before entryto college were influenced, in particular, by mon-etary considerations, these monetary influenceson student choices would not be reflected in themain study results.

For these reasons, students in the study samplewere contacted again in the fall of 1984 to obtaininformation concerning the colleges in which theyhad actually enrolled. This enrollment informa-tion was then compared with students' earlierreports concerning college choices. The mainfindings of this folk,w-up survey are summarizedbelow.

Data collection procedureIn November 1984, respondents to the earlier sur-vey stages were asked to indicate: (1) whetherthey attended college in the fall of 1984 (and, ifthey did not attend, the main reasons for notattending); (2) if enrolled in college in the fall of1984, the name of the college in which the studentwas enrolled and whether this was the same col-lege he or she had planned to attend as of theend of high school (i.e., in May/June 1984); if itwas not the same college, the main reason for thechange was requested.

Questionnaires were accompanied by a c( verletter from the president of the College Boardthanking students for taking part in the mainstudy. A brief summary of main findings was alsoenclosed as a tangible expression of appreciationand as a means of motivating response to thefollow-up.

Since our records contained students' homeaddresses but not college addresses, question-naires were sent to students' homes. The mailingwas timed to arrive just before Thanksgiving,since it was assumed that a substantial numberof those students residing at college would visithome during Thanksgiving and would thus re-ceive the questionnaire directly. For students notat home during this period, the mailing wouldhave to be forwarded to the students' campusaddresses.

91

9 7

The sample for the follow-up study included allstudents for whom college choice information hadbeen obtained in the main study. This sampleincluded: (1) students who applied to only onecollege and who were not included in the tele-phone survey (n = 325) and (2) students whoapplied to more than one college and with whomtelephone interviews were completed in May/June (n = 1.183). Thus, the total number of casesincluded in the follow-up survey was 1.508.

FindingsResponse ratesA total of 909 completed questionnaires were re-ceived from the 1,508 students in 'he follow-upsample. This represents an overall response rateof 60.3 percent. This relatively high response rateis generally consistent with the high rates expe-rienced in the earlier study phases and is aboutas high as could be expected for a mail survey ofthis kind with no follow-up to nonrespondents.This experience indicates that it is possible toobtain a reaonably high response to a survey ofcollege freshmen conducted by means of a briefquestionnaire mailed to their home addresses inthe fall.

Analyses of nonrespondents and respondentsby sex, class rank, parental income, and SATscores are provided in Table 9.1. Only negligibledifferences exist between respondents and non-respondents on each of these variables, and theseanalyses show no evidence of response bias. It isworth noting as well that the original study sam-ple of 2.000 was selected that equal numbersof cases would fall in each of five intervals foraverage SAT scores, and the follow-up respon-dents are also distributed approximately evenlyover these intervals.

Although Table 9.1 shows no evidence of non-response bias, it is possible that the variable ofintere in the follow-up study-changes in col-

98

Table 9.1. Comparison of fall follow-uprespondents and nonrespondentson selected background variables

Nonrespondents Respondents

Average SAT score550-599 19.1% 19.1%600-649 20.8 18.2650-699 19.3 19.6

700-749 21.7 20.6750-800 19.1 22.5

100.0% 100.0%

High schoolclass rank2nd tenth 18.9% 17.4%Top tenth 81.1 82.6

100.0% 100.0%

GfnderMale 63.8% 61.2%Female 36.2 38.8

100.0% 100.0%

Self-reported parentalgross income$30.000 or less 24.2% 25.6%$30.001-$49,999 36.6 37.4$50,000 or more 39.2 37.0

100.0% 100.0%

lege plans-has a relationship to response, butnot to these background variables. If studentswho changed college plans were either more orless likely to return our questionnaire. our esti-mates of incidence of such changes could bebiased.

College nonattendanceOnly 7 of the 909 respondents stated that theydid not enroll in college in the fall of 1984. Ofthese seven, only two indicated that monetaryfactors (lack of money or need to take a job) werethe main reasons for changes in college plans.

92

Four of the seven provided general/personal rea-sons (e.g., "felt I needed to take some time off").

These findings need to be related to the timeframe of our study. An additional seven studentswere not included in the fall follow-up surveybecause they stated during telephone interviewsin May or June that they had decided not to attendcollege immediately after high school. Most ofthese students had decided by that time to takeadvantage of other educational opportunities(e.g., study abroad under a student exchange pro-gram, or participation in a field study for a sci-entific project).

Changes in college choiceInformation collected in our follow-up study per-mits changes in college choice to be examined intwo ways.

First, since respondents attending college inthe fall provided the name of the colleges in whichthey had actually enrolled, the college listed onthe follow-up questionnaire could be coatparedrith the college choice reported by the studentsearlier. For students who applied to only one col-lege, the single colleges applied to were taken tobe the earlier choices. For other students, earliercollege choices were det-2rmined in telephone in-terviews conducted in May and June.

Second, students also indicated on the follow-up questionnaire whether the college enrolled inwas "the same college you were planning to at-tend, as of the end of your senior year in highschool:9

There were 902 respondents to this part of thefollow-up questionnaire: the original 909 less the7 students not attending any college. Of these902. only 9 listed different colleges in the Novem-ber follow-up survey from the ones they had in-dicated earlier. Only one of these students withdiscrepant choices was from the group initiallyreporting application to only one college. sub-stantiating the assumption that virtually all thestudents listing only one application on the March

questionnaire would ultimately attend the col-leges listed. The other eight students with dis-crepant choices listed different colleges from theones indicated as the colleges chosen at the timeof the telephone interview.

A slightly larger number (24 students) reportedthat they had changed their choice of college toattend after the end of the senior year in highschool. Of these 24 students, 5 were students whoalso listed different colleges in the spring and fall.However, 19 of these 24 students listed the samecolleges on the follow-up questionnaire as theones named as their choices in an earlier phaseof the study. The reasons given by these studentsfor changing colleges, which are reported in Ta-ble 9.2, shed some light on this apparent contra-diction.

Seven students who listed the same colleges inthe spring and fall indicated they were not ac-cepted to a preferred school from a wait list.Although they may perceive themselves as havingchanged their college choice (since they wouldhave attended a different college had they beenaccepted from the wait list), the choice reportedto us in May or June is properly consistent withthe one listed in the fall. The 12 additional stu-dents reporting changes in college choices, butlisting the same colleges in the spring and fall.

Table 9.2. Reasons given forchanges in college choice

Reason

Money-related reasonFamily movedNot accepted from

wait listAccepted from wait

list

93 99

C',llege listed in follow-up was

same as inearlier report

12

0

0

different fromearlier report

3

all gave reasons relating to college costs or finan-cial aid. We assume that these students attendcolleges that were not their most preferred col-leges, but that the decisions to do so were madeprior to the telephone interviews. Some of thesestudents may not have taken literally our questionconcerning consistency of college attended withthe "college you were planning to attend, as ofthe end of your senior year in high school."

DiscussionSeveral general conclusions are supported by thefindings of the follow-up study discussed in thischapter. With respect to college attendance, avery small percentage (roughly 1 percent) of stu-dents fike J)cise in our respondent group (SAT-taking high-ability students who filed college ap-plications in their senior year of high school) failto attend college in the fall immediately after highschool. Since nonrespondents to our initial springquestionnaire on college applications may haveincluded an additional number of students notapplying to college, this result may underestimatethe percentage of students from the populationwe sampled who do not go directly to college fromhigh school.

Those not attending college are made up pri-marily of students deferring college study eitherto pursue other ducational opportunities or totake time off for ,ersonal reasons.

While almost no students in our sample re-ported not enrolling in any college due to lack ofmoney, this finding needs to be interpreted incontext. Our sample did not include students whohad not applied to colleges or who had not takenthe SAT because they had already ruled out goingto college, whether because college going wasperceived to he too costly or for other reasons.

With respect to changes in college plans follow-ing high school graduation, students reporting inMarch application to and acceptance at only onecollege will almost certainly enroll in the collegenamed. For students choosing among two or more

100

admissions offers, choices made by May to lateJune are very likely to be followed through. Onlya tiny fraction of students enroll in different col-leges from the ones named as final choices intelephone interviews in May and June.

The findings of this follow-up survey validateto a very large degree the college choice dataanalyzed in the main study. Overwhelmingly, stu-dents enrolled in the schools they had reportedearlier as their choices. Neither monetary norother reasons caused many students to changefrom college choices reported in May and June.

Th.,. findings of this follow-up survey appear tobe at variance with reports of college admissionsofficers that significant numbers of students si-multaneously submit deposits to hold multipleplaces in colleges and ultimately fail to enroll inone or more colleges whose admissions offersthey have acceptedthe "no-show" phenome-non. Since these reports are certainly accurate,we believe that our contrary finding of a low in-cidence of changes in college choice is most likelya function of the timing of and procedures for thetelephone interviews. Students in our samplewere called starting the second week of May.Only students stating they had made a choice ofcollege to attend were interviewed, with otherstudents called back at a later date. Callbacksfor some students extended into mid-to-late June.Thus, our data are not inconsistent with theknown fact that a sizable minority of studentsaccepted to selective colleges defer decisionspast the beginning of May. Experience in the in-terview portion of the study and in this follow-upsuggests, however, that stable choices have beenreached by nearly all students like those in oursample by the end of June. It appears that sur-veys during the May and June period can capt irereports of college choices that are the same asfall enrollment decisions for about 98 percent ofsuch students.

Appendix 1. An overview of themultinomial logit mod&

In this appendix, we provide a brief descriptionof the multinomial logit model that is used exten-sively in this study. Also, some Iwy statisticaldetails and tests associated with using this modelare described. For further details of the model asapplied in the college choice context, the inter-ested reader is referred to Kohn, Manski, andMundel (1976), Chapman (1977, 1979), Punj andStaelin (1978), and Manski and Wise (1983).Technically oriented readers may wish to consultMcFadden (1974), Gensch and Recker (1979),Hensher and Johnson (1981), Maddala (1983), andBen-Akiva and Lerman (1985) for more extensivediscussion of the multinomial logit model. A par-ticularly complete, up-to-date, and applied treat-ment of discrete choice models is provided inBen-Akiva and Lerman (1985).

The modelThe multinomial logit model expresses the prob-ability of choosing an alternative (e.g., a college)from a choice set (e.g., all colleges to which astudent has been admitted) as depending on therelative value or utility of the alternative com-pared to other available alternatives. The multi-nomial logit model is a well-defined probability-of-choice model: each alternative will have a

non-negative (zero or positive) chance of beingchosen, and the sum of the probabilities acrossall alternatives in a choice set will be equal to1.0. Specifically, the mathematical form of themultinomial logit model is as follows:

exp( Vi))P =" exp(Vi) + exp(Vi,) + + exp(Vi ji)

(Al)where

Ji

vii

a decision-maker (a student)an alternative (a college)the total number of alternatives (colleges) inthe choice set of decision-maker (student) ithe probability that decision-maker (student) ichooses alternative (college) jthe overall value or utility which decision-maker (student) i derives from alternative (col-lege) j

exp(-) the exponentiation function.

To operationalize this model. the form of thevalue or utility function. V, muFt be specified. Alinear additive functional form is typically as-sumed, although it is important to note that (a)the model itself is of a nonlinear form, due to thepresence of the exponentiation functions; (b) thevariables themselves may be nonlinear compo,i-tions or interactions of other variables; a;ai (c)linear additive functional forms are often parsi-monious (simple) representations of more com-plicated functional relationships. especiallywithin a limited relevant range of variation in a

" 101

sample of data. Assuming that there are K rele-vant variables which the decision-makers (stu-dents) implicitly combine to form overall value orutility assessments of each alternative (college).V may be defined as follows:

vii = 01Z,i1 + + OhZ ijk + + °KZ ijK(A2)

where

OA the relative importance of attribute k to the de-cision-makers (students) in forming their (,verallvalue judgments about the worth of an alternative(college)

Zo the numerical value of at lute k associated withalternative college) j to decision-maker (student)

The relative importance weights O. -, Ok arethe parameters to be estimated. In the collegechoice context, the Z variables may include suchfactors as college characteristics (such as the sizeof a college or its tuition level), perceptual ratingsof colleges (such as the perceived quality of acollege by a student), and individualinstitutioninteractions (such as the amount of scholarshipaid awarded by a college to a student).

As a statistical model, the multinotrial logitmodel possesses a number of desirable features.First, it represents a choice process in a naturalfashion. Students are viewed as making a specificchoice from among a given (and specific) set ofcolleges. Second, it is a natural probabilisticchoice model. The probabilities derived satisfythe usual laws of probabilities (non-negativity andsumming to 1.0). Third, the statistical propertiesof the parameter estimates are familiar. In partic-ular, they are (asymptotically) normally distrib-uted, so standard tests of statistical significanceabout the estimated relative importances can bemade. Fourth, the probabilistic choice model al-lows strong statements to be made about the mag-nitude of the influence of the variables influencingchoice. For example, the model will providequantitative estimates of the trade-offs between

102

financial aid and choice probabilities. Thus, it ispossible to derive an estimate of by how muchchoice probabilities (or, in the aggregate, marketshares) will change with changes in financial aidoffered to students.

Estimation of the multinomiallogit model's parametersMaximum-likelihood techniques are uscd to es-zimate the parameters of the multinomial logitmodel. This essentially involves a series of non-linear regressions, where the maximum-likeli-hood technique attempts to choose values of 0such that the statistical fit between the observedchoices and the predicted choices is maximized.

In our study, students reported on the rankorder of their three most preferred colleges at theapplication stage (the unconstrained prior pref-erence measures). At the choice stage, they wereasked to indicate their chosen college, plus theirsecond and third choices. By asking students toindicate their second and third preferences/choices, efficient estimation of the multinomial-logit-model parameters may be achieved by usingthe explosion techniques described in Chapmanand Staelin (1982) This explosion procedure in-volves generating extra choice observations fromthe ranked preference/choice data for each re-spondent. Extra observations (choice sets) im-prove the statistical precision of the (multinomiallogit) model's parameter estimates (relative im-portances). Exact statistical testing proceduresexist to determine if such explosion proceduresmay be used. The key condition to be satisfiedbefore invoking the explosion procedure is thatthe students' relative importances must be (sta-tistically) identical for first-choice and for subse-quent lower-choice decisions.

Statistical goodness-of-fit analysisThe most frequently used statistical goodness-of-fit measure for multinomial logit models is the

96

Table Al .1. Reported log-likelihood ratio index statistics in previouscollege choice studies

Reportedlog-likelihoodratio index statistic

Samplesize

Number ofvariables inchoice model

Kohn, Manski, and Mundel (1976)Illinois students

Low income 0.382 997 15Medium income 0.286 990 15High income 0.269 1028 15

North Carolina studentsLow income 0.272 1623 15Medium income 0.302 749 15High income 0.319 760 15

Chapman (1977, 1979)High-income students

Engineering and science 0.128 1152 10Liberal arts 0.097 532 10Fine arts 0.146 513 10

Medium- and low-income studentsEngineering and science 0.158 1012 12Liberal arts 0.162 183 12Fine arts 0.160 278 12

Note: "Sample size refers to the number of choice sets available for analysis.

log-likelihood ratio index (LLR1), which is definedas:

LL(0 = 0*)LLRI = 1 (A3)LL(0 = 0)

where LL(0 = 0*) is the value of the log-likelihoodfunction at the maximum-likelihood estimate 0*(sometimes called the final log-likelihood [finalLI..] value) and LL(0 = 0) is the value of the log-likelihood function evaluated at the point 0 = 0(sometimes called the initial log-likelihood [Ini-tial LL] value). LLRI is bounded by 0 and 1; thusit has an analogous interpretation to R2 in stan-dard regression analysis.

Reported values of LLRI from some previouscollege choice studies which used the multino-

mial logit model are displayed in Table A1.1. Therange of values is about 0.09 to 0.38. The base ofcomparison in calculating the LLRI is the equi-probable choice modela model in which e,,eryIlternative has an equal chance of being chosen.Given the nature of the college choice processwith extensive search for satisfactory college al-ternativesthis is quite a strong base model.Thus, while modest improvements over this equi-probable model are undoubtedly possible, itshould not be expected that perfect models wouldever be developed (i.e., models with LLRI valuesnear 1.0). Indeed, the data reported in Table A1.1substantiate this observation.

The LLRI value from the study by Manski andWise (1983) is not reported in Table A1.1. Manski

97. 1 03

and Wise (1983, p. 111) included four noncollegealternatives in their college choice model: (1) la-bor force participation (the full-time working op-tion); (2) military enlistment; (3) homemaking;and (4) a combination of part-time school andpart-time work. Alternative-specific indicatorvariables (dummy variables) were used in theirmodel to account for these noncollege options.These variables had substantial effects in theirmedel (t-ratios of 5.3 to 14.6). The inclusionof these noncollege options makes their collegechoice model fundamentally different from thosein Kohn, Manski, and Mundel (1976) and Chap-man (1977. 1979). Thus, the LLRI value of 0.501reported in Manski and Wise (1983) is not com-parable to the other LLRI values from pure, col-lege choice studies.

Other goodness-of-fit measures are sometimesused to describe how well the multinomial logitmodel performs. The correlation of actual andpredicted choices (aggregated across all choicesets) provides another useful measure of perfor-mance of the model. Punj and Staelin (1978) re-port the results of an external predictive-validityassessment. where they used a multinomial logitmodel to predict the choices of the followingyear's students. Their predictions were excellentapproximations of actual enrollment patterns.

Hypothesis testing andpooling testsStandard types of hypothesis tests may be usedto test the statist;cal significance of individualparameter estimates in the multinomial logitmodel. For example. the traditional t-ratio (theratio of a coefficient estimate to its standard error)may be employed to test whether an individualcoefficient is different from zero.

We conduct a number of pooling tests in thisstudy. To test the hypothesis that N groups ofchoice data are characterized by the same un-derlying parameter vector (including the same

104

variables), a standard pooling-test procedure isfollowed. The model is estimated separately foreach of the N groups and then a single pooledmodel is also estimated. The relevant test statis-tic is:

2 {LL (0) ILL (0) + + LL (13;) ++ LL (OZ)j}

where WO!) is the maximum log-likelihoodfunction value for the pooled data and LL (9.*)is the maximum log-likeliEood function value forsubgroup n. This test statistic is asymptoticallydistributed chi-squared with K(N 1) degrees offreedom, where K is the number of parametersestimated in each model (Wald 1)43; Watson andWestin 1975; Ben-Akiva and Lerman 1985, pp.194-204). To use this pooling est in this preciseform, each of the subgroups of choice sets mustbe characterized by the same variables as thepooled data. Other issues associated with suchpooling testing are discuss,!d in Ben-Akiva andLerman (1985, pp. 194-204). We use poolingtests such as this to examine the explosion pos-sibilities inherent in rank-ordered choice sets(Chapman and Staelin 1982) and also to test forindividual differences.

98

Appendix 2. The mail questionnaire

This appendix contains a copy of the questionsused in the mail questionnaire that was employedin this study. The questions are in the exact orderin which they were arranged -In the actual ques-tionnaire. A mailing label wid the student's ad-dress was included at the top. The initial intro-ductory instructions/sentences were as follows:"We need the information on the label below inorder to relate your responses to this questionaireto other information you have previously providedto the College Board. If any of this information isincorrect, please give the correct information inthe space to the right of the label."

" 1 05

Question 1: To which colleges have you applied? Please list these colleges below andprovide the other information requested for each college.

Application status at this time Financial aid

Haven'tColleges applied to heardCollege CitylState yet Accepted

Notaccepted

Onthe

waitlist

Did you(or will you) app'y

for financial aid?[circle Yes or No]

0 0 0 0 Yes No0 0 0 0 Yes No0 0 0 0 Yes No0 0 0 0 Yes No0 0 0 0 Yes No0 0 0 0 Yes NoE 0 0 0 Yes No0 0 0 0 Yes No0 0 0 0 Yes No0 0 0 0 Yes No

Note: If you have applied to any college under an early action or early decision plan, but adecision on your application has been deferred until a later notification date, pleasemark the column "Haven't Heard Yet."

Question 2: Assume that you will be accepted at all the colleges you listed and the cost toyou and your family would be about the same at any of these colleges (andtherefore not a factor in your choice).Then, which of these colleges would be your:

First Choice.Second Choice.

Third Choice:

1P6100

Question 3: Please list other colleges that you did not apply to, but to which you gaveserious consideration. For this question, "serious consideration" means thatyou did something more than just thinking about applying. For example,include colleges in this group if you sent away for information from the collegeor for application materials, or if you were interviewed by a representative oralumnus/a of the college, or if you visited the campus, or if yeu took somesimilar action. (List up to five colleges.)

College CitylState

Question 4: Thinking about the colleges that you listed or other colleges that you considered,is there one that you did not apply to for a particular reason, but that mightotherwise have been one of your top choices?

YESLJ NOLJIf "yes," what college? (If more than one, give only the one most preferred.)

College: City/State-

What is the main reason that you did not apply to this college?

Question 5: Were you influenced to apply to certain colleges because their policies are toprovide sufficient financial aid to permit any accepted student to attend?

Li This was very important.This was somewhat important.This was not important.

Question 6: Were you influenced to apply to certain colleges because they offer scholarshipsto students with high academic achievement (regardless of need)?

This was very important.This was somewhat important.

0 This was not important.

101 1 7

Question 7: Some factors that students typically consider when choosing among collegesare listed below. Please indicate how important each of these factors is to youin choosing a college. Please circle one of the numbers for each of the factorslisted below.

Factors Degree of importance

Academic diversity (range of coursesoffered)

Academic facilities (library, computer re-sources, laboratories)Geographical location (part of country,distance from home)

Overall academic reputationLow overall costs (tuition, fees, roomand board, other expenses)Social climate (college atmosphere, whatthe student body is like, how I would fitin)

Availability of special majors, degrees, orhonors programsCommunity setting (urban, suburban,small town, rural)

Preparation for career or graduate andprofessional school opportunitiesAvailability of financial aid

Personal contact with college reprecenta-tives (admissions staff, faculty, coaches,others)

Academic strength in your major areasaf interestEmphasis on undergraduate education(small classes, faculty contact)Opportunities for involvement in extra-curricular activities (clubs, sports, per-forming arts, journalism)

Notimportant

Somewhatimportant Important

Veryimportant

1 2 3

_

4

1 2 3 4

1 2 3 4

1 2 3 4

1 2 3 4

1 2 3 4

1 2 3 4

1 2 3 4

1 2 3 4

1 2 3 4

1 2 3 4

1 2 3 4

1 2 3 4

1 2 3 4

108102

Question 8: In this question, we are interested in how you rate your top three collegechoices (that is, the colleges that you listed in Question 2). Please rate eachof these colleges on the factors listed below. Circle the grade that you wouldassign to each college on each factor, where:

a "grade" of A means that you believe that the college is excellenta "grade" of B means that you believe that the college is gooda "grade" of C means that you believe that the college is faira "grade" of D means that you believe that the college is poora "grade" of F means that you believe that the college is unacceptable.

Please fill in the column headings with names of the colleges you listed inQuestion 2. If you applied to only one or two colleges and, therefore, gavefewer than three top cho.cPs, rate only the one or two colleges to which youapplied. Circle the "grade" that you would assign to each of these colleges oneach of the listed factors. Even if you aren't sure, please answer in terms ofyour impressions of the colleges.

First Second ThirdChoice Choice Choice

Factors [ I [

Academic diversity (range of courses offered) ABCDF ABCDF ABCIJFAcademic facilities (library, computer resources, A BC DF ABC DF AB C DF

laboratories)

[other factors as listed in Question 7]

Question 9: Are there any major factors that you consider important in choosing a collegethat were not listed in the preceding questions? Use this space for additionalcomments you would like to make.

Appendix 3. The telephone interviewinstrument

The content and wording of the questions for thetelephone interviews are described in this appen-dix. The actual interview form used was morecomplex than that presented here due to skippatterns and an elaborate format for recordingadmissions, financial aid, and other data for mul-tiple colle&s for each respondent. This appendixdescribes the interview content in an easier-to-follow format.

A "response grid" was used to record many ofthe answers to the repetitive questions related tothe multiple colleges to which che respondentshad applied. This grid was in the form of a matrix,with the rows corresponding to the colleges andthe columns corresponding to the specific ques-tions/responses of interest. The use of the gridenabled the telephone interviews to be adminis-tered in an efficient manner.

In the questionnaire below, instructions to thetelephone interviewers are shown in brackets.

Screening section

Good [morning, afternoon, evening], this is [your (interviewer's)name] calling for the College Board to follow up on the questionnaire you filled out for usrecently.

Have you made your final decision about which college you will attend?Yes [go to Question 11No

[If "No"] When do you expect to make your final decision?

We'd like to talk to you aftt.r you've made your decision. We'll call back in a week or two.

What's the best time and day to reach you at home'?

Thanks for helping us with the study. Good-bye.

104

110

Admission status by college, whether aid applied for or not

Question 1:

Question 2:

Which college are you planning to attend?

[Record answer on response grid.]

I'd like to check the current status of all your college applications. As I mentionthem, tell me if you were accepted, not accepted, put on a wait list, or havenot yet heard. How about [a college]?

[Read list of up to 10 colleges student reportedapplying to at time of mail surveyand record admission status on grid.]

Question 3: Did you apply for financial aid at any of these colleges?YesNo

[If "Yes," record in grid for applicable colleges.]

Question 4: Have you applied to any other colleges?

Yes [Continue on to Question 5.]No [Skip to Question 8.]

Question 5: Which ones?[Record additional colleges applied to.]

Question to: Have you heard from these colleges?

[Record admissions status for additional colleges.]

Question 7: Did you apply for financial aid at any of these colleges?YesNo

[If "Yes," record in grid for applicable college(s).]

Question 8:

Question 9:

Did either of your parents attend any of the schools you applied to?[If "Yes," record in grid for applicable college(s).]

[Ask if accepted by more than two colleges.]After [College planning to attend], which of the schoolsthat accepted you was your second choice?

[Record answer on grid.][Ask if accepted by more than three colleges.]Which of the schools that accepted you was your third choke?

[Record answer on grid.]

111

Portable scholarships

Question 10: Have you been awarded any scholarships which you could use at any schoolyou decided to attendsuch as a National Merit Scholarship or one awardedby a corporation or private organization?

YesNo [Go to Question 14.]

[If "Yes," record source for up to five portable scholarships.]

Question 1: How much will this scholarship provide for your freshman year?[Ask and record on portable aid grid for up to five scholarships.]

Question 12: After your first year, is there any possibility of renewing this award for yourlater college years?

Definitely notSome possibilityDon't know, unsure

[If "some possibility," ask Question 13.]

Question 13: Which is most accurate?There is only a possibility it may be renewed.You can count on it, if you maintain a required GPA.It is definitely guaranteed without any conditions.

[For each portable scholarship, record following categories ongrid for renewal possibilities from response to Questions 12and 13: "None," "Possible," "Count on it," and "Guaranteed."]

College financial aid awards

Question 14: Have you been awarded any financial aid or scholarships by any of the collegesyou applied to?

YesNo [Skip to Question 19.]

Question 15: Which colleges offered you financial aid (and/or scholarships)?[Record on aid grid for up to 10 colleges.]

[Questions 16, 17, and 18 are to be repeated for each college awarding the student financialaid.]

1 2 106

Question 16: What was the dollar value of the total financial aid package offered you by[Read each college name. one at a time]?

[Record amounts on aid grid.]

Question 17: Of that total package, how much was in the form of grants and scholarships.how much in loans, and how much in a job?

[Record amounts on aid grid.]

Question 18: If you were to accept that financial aid package, would you expect that thegrant or scholarship portion . . .

Would definitely not be renewed in hture years?Might possibly be renewed?Will be renewed if you maintain a required CPA?Is definitely guaranteed without conditions?

[Record renewability response (1, 2. 3. 4) on aid grid.]

FF ctors in college choice

Question 19: On the questionnaire you returned, you told us how important certain factorswere to you in choosing a college. I'd like to ask you how you feel about afew of these factors, now that you have actually made a decision.As I read each one, please give me an answer from 1 to 4, where 1 meansthe factor was "not important," 2 means it was "somewhat important,- 3means it was "important," and 4 means it was "very important" to you inmaking your final decision.

[Respondents randomly assigned to Form A or Form B.]

Form AFor example, how important was . . . [use random start]

Academic diversity (range of courses offered)?Geographical location (part of the country, distance from home)?Low overall costs (tuition, fees, room and board, other expenses)?Availability of special majors, degrees or honors programs?

Preparation for career or graduate and professional school opportunities?Personal contact with college representatives (admissions staff, faculiy,coaches. others)?Emphasis on undergraduate education (small classes, faculty contact,etc.)?

1 1 3

Form B

For example, how important was . . . [use random start]Academic facilities (library, computer resources, laboratories. etc.)?

Overall academic reputation?Social climate (college atmosphere, what the student body is like. how Iwould fit in)?Community setting (urban, suburban, small town, rural)?Availability of financial aid?Academic strength in your major areas of interest?

Opportunities for involvement in extracurricular activities (clubs, sports,performing arts, etc.)?

[Repeat Question 20 for each of the seven choice factors rated in Question 19.]

Question 20: Now, thinking about [a choice factor from question19], using the grades A for "Excellent," B for "Good," C for "Fair," D for"Poor," and F for "Unacceptable," how would you grade[initial first-choice college] on [choice factor]?

And how would you grade [initial second-choicecollege] on this factor?

How about [initial third-choice college]?

[Record responses on grid.]

Contacts with colleges

Question 21: Before you made your final college choice, did you have any contact with anyof the colleges which accepted you, after the initial acceptance letter? Forexample, did you receive any personal letters from staff members or alumni?

YesNo [Skip to Question 24.]

Question 22: Which [staff members, alumni] from which schools wrote you letters?[Record on grid for each applicable collegeby each type of person contacting:

President/DeanFacultyCoachStudentMumni

1 1 4

108

Admissions officerHonors programOther]

Question 23: Did any of these letters have a particularly positive or negative influence onyour decision about where to go to school?[If "Yes"] Which letters had an influence?

[Circle + or on response grid.]

Question 24: Have any college staff members or alumni called you since you received youracceptance letter?

YesNo [Skip to Question 27.]

Question 25: Which [staff members, alumni] from which schools called you?[Record on grid for each applicable collegeby each type of person contacting:

President/DeanFacultyCoachStudentAlumniAdmissions officerHonors programOther]

Question 26: Did any of these calls have a particularly positive or negative influence onyour decision about where to go to school?[If "Yes"] Which calls had an influence?

[Circle + or on response grid.]

Question 27: Did you meet with any college staff members or alumni after you wereaccepted?

YesNo [Skip to Question 30.]

Question 28: Which [staff members, alumni] from which schools met with you?[Record on grid for each applicaUc collegeby each type of person contacting:

President/DeanFaculty

1 1 5109

CoachStudentAlumniAdmissions officerHonors programOther]

Question 29: Did any of these meetings have a particularly positive or negative influenceon your decision about where to go to school?[If "Yes"] Which meetings had an influence?

[Circle + or on response grid.]

Question 30: Did you receive any additional descriptive literature about any of the collegeswhich accepted you?

YesNo [Skip to Question 32.]

Question 31: Which colleges sent you descriptive literature?[Record on grid.]

Question 32: Did you attend any parties for accepted candidates sponsored by alumni orother college representatives?

YesNo [Skip to Question 34.]

Question 33: Which colleges sponsored parties which you attended?[Record on grid.]

Question 34: Have you visited the campuses of any of the colleges which accepted youeither before or after you were accepted?

YesNo [Skip to Question 36.]

Question 35: Which colleges did you visit?[Record on grid.]

Question 36: Did any of these activities (receiving literature, attending parties, or visitingcampuses) have a particularly positive or negative influence on your decisionabout where to go to school?[If "Yes"] Which activities had an influence?

[Circle + or on response grid.]

1110

Academic bas-mi for scholarships

Question 37: [Ask only if respondent was offered scholarship by any college.] Was all orany part of the scholarship(s) you were offered by any college awarded foryour academic performance?

YesNo [Skip to Question 44.]

Question 38: Which colleges offered you scholarships based on your academic qualifica-tions?

[Record on grid.]

Question 39: For the academic scholarship offered you by wereyou required to submit any special application or other written materials orhave an interview specifically related to the scholarship award?

[Record "Yes" = 1, "No" = 2 on grid.]

Question 40: Were you invited to any type of on-campus ceremony to receive yourscholarship from which involved an overnight or weekend stay?

[Record "Yes" = 1, "No" = 2 on grid.]

Question 41: Did you receive any of the following relating to this scholarship (or would youhave received them if you had accepted the award): an award or plaque; aninvitation to a special reception or dinner in your home area; any specialrecognition planned for your high school graduaf, )n; or any other symbolicrecognition of achievement?

[Recot d "Yes" = 1, "No" = 2 on grid.]

Question 42: If you [accept, had accepted] this scholarship, [will, would] you be part ofany honors program or special group next year at college, along with otherscholarship winners?

[Record "Yes" = 1, "No" = 2 on grid.]

Question 43: [Ask if respondent answered "Yes" to any questions 39-42.] Did any of theserequirements, honors, or special events have a significant positive or negativeinfluence on your decision about where to go to college?[If "Yes"] Which events, what influence?

[Circle + or on response grid.]

11. 7

Self-reports on change in college choice

Question 44: [Ask if respondent is not going to attend the top college (Highest prior-preference college) to which he or she was admitted.]In the mail questionnaire you sent us. you indicated that[top admitted scho-1 was one of your top choices. What was the one mainreason you chose to go to a different school?

[Record up to three reasons.]

Question 45: [Ask if respondent was admitted to more than one college.] Think about theschool you decided to attend and your second-choice school. Suppose yoursecond-choice school offered you an extra 8500 scholarship. Would that havechanged your decision?How about if they offered an extra $1,000?How about an extra $2,000?How about an extra $3,000?

[Record 1 = "Yes," 2 = "No" on response grid.]

[If "Yes" to any of these questions, skip to closing section.]

Closing Section

Thank you for your cooperation in the study. That's all the questions we have for you.

Appendix 4. An illustrative choiceprobability calculation

In this appendix, we illustrate the use of the mul-tinomial logit model and our estimates of its pa-rameters (relative importances of the variables)in calculating choice probabilities in various sam-ple situations. These situations/examples/scena-rios are described in the latter part of Chapter 4.

Consider the situation below:

Choice set Three colleges, denoted as colleges A. B. and C. (College A will be constructedcomposition to be an average college. B will be a public institution. and C will be an average

top-seven school.)

Prior preference Colleges A, B. and C are the first. second, and third prior preference alternatives.situation respectively.

Financialconsiderations

College-specificconsiderations

Other relevantfactors

The COSTS. GRANTAID. and OTHERAID situations are as follows:

COSTS GRANTA1D OTHERA1DCollege A $10.500 11.240 500College B 5.500 16 0 0College C $14.000 83.000 $2.000

Colleges A and B are not top-seven schools: College C is an average top-seveninstitution.

The mean SAT scores of students at colleges A. B. and C are 550. 500. and 600.respectively. Assume that the student has an SAT score of 675. Perceived renew-ability of the financial aid is "probable" at college A (RENEWAL = 3. RENEWM

0) And "possible" at college C (RENEWAL = 2. RENEWM = 0). Renewabilityof aid is not relevant at college B (RENEWAL = 0. RENEWM = 1). since no aidwas offered in the first instance.

113

119

Table A4.1. Details of the illustrative choice probability calculation

Weight'

College A College B College C

Valueofvariable

Partialutilityscore

Value ofvariable

Partialutilityscore2

Value ofvariable

Partialutilityscore

FIRST 3.2762 1.000 3.2762 0.000 0.0000 0.000 0.0000SECOND 1.9061 0.000 0.0000 1.000 1.9061 0.000 0.0000THIRD 1.3063 0.000 0.0000 0.000 0.0000 1.000 1.3063COSTS 0.1313 10.500 1.3786 5.500 0.7221 14.000 1.8382COSTSM 0.0400 0.000 0.0000 0.000 0.0000 0.000 0.0000TOTALAID 0.0770 0.000 0.0000 0.000 0.0000 0.000 0.0000GRANTAID 0.2907 1.240 0.3605 0.000 0.0000 3.000 0.8721OTHERAID 0.0158 0.500 0.0079 0.000 0.0000 2.000 0.0316RENEWAL 0.3062 3.000 0.9186 0.000 0.0000 2.000 0.6124RENEWM 0.6075 0.000 0.0000 1.000 0.6075 0.000 0.0000SATFIT 0.0041 125.000 0.5125 175.000 0.7175 75.000 0.3075SATM 0.0631 0.000 0.0000 0.000 0.0000 0.000 0.0000COLLEGE' 1.1546 0.000 0.0000 0.000 0.0000 1.000 1.1546

Total utility score4 2.6721 1.0740 1.8313Adjusted utility scores 14.4703 2.9271 6.2420Probability of choice6 0.6121 0.1238 0.2641

1. With the exception of the variable COLLEGE. the "Weight" values are the coeffic.-::- _.F.timates id. the multi-nomial logit model. They are taken directly from the results reported in Table 4.9. The weights are the estimatedvalues of the 8 parameters in equation tA2) in Appendix 1.2. "Partial utility score" is the product of the weight and the "Value of variable." The partial utility scores are theindividual terms OAZA in equation (A2) in Appendix 1.3. "COLLEGE" refers to an average top-sven college: its weight is the mean college-specific coefficient estimatefor the top-seven colleges as reported in Table 4.9.4. "Total utility score" is equal to the sum of all the partial-utility-score values fora college alternative. Total utilityscore is the V6 term in equations (Al) and (A2) in Appendix 1.5. "Adjusted utility score" equals the exponential of total utility score. For example, the adjusted utility score ofcollege A is equal to exp(2.6721) = 14.4703.6. The "probability of choice" for an alternative is equal to its adjusted utility score divided by the sum of all theadjusted utility scores of the college alternatives in the choice set. For example. the probability of choice of collegeA is equal to 0.6121 = 04.4703104.4703 + 2.9271 +6.242011. See equation tAll in Appendix 1.

The details of the choice-probability calculationsare shown in Table A4.1. As may be noted, theestimated choice probabilities for colleges A. B,and C are approximately 0.61 (61 percent), 0.12(12 percent), and 0.27 (27 percent), respectively.

In this situation, note that being first choice ona prior preference basis propels college A well

ahead of the others. The considerable advantagethat college B has over college C due to being thesecond choice on a prior preference basis is offsetby B's much poorer SATFIT and the scholarshipaid offered by college C. Also, the top-seven ef-fect has a considerable impact on the choiceprobability for college C.

120114

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Other titles in this series:

Organizational Measurement and Its Bearing on the Study ofCollegeEnvironments. Research Monograph No. 2. Allen H. Barton; intro-duction by Paul F. Lazarsfeld. (254730) 1961, 91 pages, $5.

Career Developmeru: Choice and Adju.stment. Research MonographNo. 3. David V. Tiedeman and Robert P. O'Hara. (213810) 1963,115 pages, $7.95.

Career Developmeru: Self-Concept Theory. Research MonographNo. 4. Donald E. Super, Reuben Starishevsky, Norman Matlin, andJean Pierre Jordaan. (213815) 1963, 104 pages, $6.

Personality Measures in Admissions: Aruecedent and PersonalityFactors as Predictors of College Success. Research MonographNo. 5. Morris I. Stein. (270500) 1963, 76 pages, $5.

The Measurement of Writing Ability. Research Monograph No. 6.Fred I. Godshalk, Frances Swineford, and William E. Coffman.(251700) 1966, 92 pages, $6.50.

Using Self-Reports to Predict Student Peormance. Research Mono-gaph No. 7. Leonard L. Baird. (251701) 1976, 92 pages, $5.

Population Validity and College Entrance Measures. Research Mon-ograph No. 8. Hunter M. Breland. (270501) 1979, 104 pages,$7.50.

Assessing Student Characteristics in Admissions to Higher Educa-tion: A Review of Procedures. Research Monograph No. 9. HunterM. Breland. (001389) 1981, 134 pages, $10.95.

Orders accompanied by either a check made payable to the CollegeBoard or an institutional purchase order may be sent to:

College Board PublicationsBox 886, New York, New York 10101

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