STATISTICAL AND METHODOLOGICAL CONSIDERATIONS FOR EXAMINING PROGRAM EFFECTIVENESS Carli Straight, PhD and Giovanni Sosa, PhD Chaffey College
RP Group Conference Presentation April 1, 2013
Pitfalls of Significance Testing
Assessment Item Number Correct
Pretest Number Correct
Posttest Statistically Significant?
Item 1 19 24 No
Item 2 12 16 No
Item 3 26 30 No
Item 4 7 10 No
Item 5 13 21 No
Item 6 5 13 No
Item 7 10 15 No
Item 8 6 16 No
Item 9 3 15 No
Avg. Correct 5.00 7.50 No
N = 30
Pitfalls of Significance Testing
NSSE Benchmark
Sample University N > 1000
Comparison Group N > 10,000
Statistically Significant?
Level of Academic Challenge
65.8 55.6 Yes
Active and Collaborative Learning
57.7 50.1 Yes
Student-Faculty Interaction
42.8 41.2 Yes
Enriching Educational Experiences
44.0 39.8 Yes
Supportive Campus Environment
62.7 56.9 Yes
Adapted from NSSE (2008)
Pitfalls of Significance Testing
2.29
3.15 3.47
0.00
1.00
2.00
3.00
4.00
Low SE Medium SE High SE
N = 187 N = 408 N = 200
N = 795
Avg.
Gra
de (G
PA S
cale
)
p < .01
p < .05
p < .01
Significance Testing: Conclusions
P-values = Sample Size x Effect Size
Greatly influenced by sample size Do not speak to the magnitude of the difference Not well understood – even by ‘experts’
Practical Significance: Effect Size
Effect Size comes in various forms Standardized (d, r)
Cohen’s conventions:
d = .20 – small; .50 – moderate; .80 – large r = .10 – small; .30 – moderate; .50 - large
Discipline specific Aspirin Example (Rosenthal & Dimateo, 2002)
pooled
CT
sXXd −
=( ) ( )
211
21
22
12
−+−+−
=nn
nsnss ctpooled
Effect Size Examples
Assessment Item Number Correct
Pretest Number Correct
Posttest Statistically Significant?
Effect Size (d)
Item 1 19 24 No .37
Item 2 12 16 No .27
Item 3 26 30 No .75
Item 4 7 10 No .22
Item 5 13 21 No .55
Item 6 5 13 No .60
Item 7 10 15 No .34
Item 8 6 16 No .71
Item 9 3 15 No .93
Avg. Correct 5.00 7.50 No .61
N = 30
Effect Size Examples
NSSE Benchmark
Sample University N > 1000
Comparison Group
N > 10,000
Statistically Significant?
Effect Size (d)
Level of Academic Challenge
65.8 55.6 Yes .72
Active and Collaborative Learning
57.7 50.1 Yes .44
Student-Faculty Interaction
42.8 41.2 Yes .08
Enriching Educational Experiences
44.0 39.8 Yes .23
Supportive Campus Environment
62.7 56.9 Yes .30
Adapted from NSSE (2008)
Effect Size Examples
2.29
3.15 3.47
0.00
1.00
2.00
3.00
4.00
Low SE Medium SE High SE
N = 187 N = 408 N = 200
N = 795
Avg.
Gra
de (G
PA S
cale
)
d =.86
d = .35
d = 1.19
Wilson’s Effect Size Calculator
http://mason.gmu.edu/~dwilsonb/ma.html
Odds Ratios
Reflect a comparison of the relative odds of an occurrence of interest given the exposure to a variable of interest
OR = (A/B)/(C/D)
Successful Not
Successful Total
Medium SE 392 26 418
Low SE 145 52 197
OR = 15.077/2.788 = 5.40
Odds Ratios
Interpreting Odds Ratios: OR = 1.50 – small; 2.50 – moderate; 4.25 – large
OR = 1 => Intervention does not affect odds of outcome
OR > 1 => Intervention associated with higher odds of outcome
OR < 1 => Intervention associated with lower odds of outcome
Converting Odds Ratios to ds and vice versa:
[ ] 81.1ln ÷= ORd )*81.1( deOR =
Working with Beta Weights
Predictor B (SE) Beta
Self-Efficacy (Post)** .09 (.01) .42
Age Range** .13 (.03) .18
Af. American vs. Others* -.31 (.15) -.08
Hispanic vs. Others -.14 (.09) -.07
First-Gen Status .06 (.08) .03
Asian vs. Others .10 (.16) .03
Gender -.01 (.08) -.002
Work Hours <.01 (<.01) .005
R2= .22 *p < .05; **p < .01
Predictors of Course Performance among Fast Track Students Completing both the Pre and Post-Test Self-Efficacy (SE) Measure (N = 623)
Working with Beta Weights
Predictor B (SE) Beta Zero-Order r Semi-Partial r Effect Size |d|
Self-Efficacy (Post)** .09 (.01) .42 .42 .41 .90
Age Range** .13 (.03) .18 .19 .18 .36
Af. American vs. Others*
-.31 (.15) -.08 -.05 -.07 .14
Hispanic vs. Others -.14 (.09) -.07 -.12 -.05 .10
First-Gen Status .06 (.08) .03 .05 .03 .05
Asian vs. Others .10 (.16) .03 .07 .02 .04
Gender -.01 (.08) -.002 -.11 -.002 .004
Work Hours <.01 (<.01) .005 .05 .005 .01
Predictors of Course Performance among Fast Track Students Completing both the Pre and Post-Test Self-Efficacy (SE) Measure (N = 623)
R2= .22 *p < .05; **p < .01
Basic Steps to Designing a Study that Measures Program Effectiveness
Example: How Do Students Perform in Fast-Track Courses? Select a reference point
Compared to whom/what?
Define what is meant by performance Course completion rate? Course success rate? Retention rate? Other?
Select appropriate statistical analysis Conduct analyses and write up results
Select Comparable Cohorts
Determine what/whom performance outcomes will be measured against
Goal is to select two cohorts that are the same in as many
ways as possible, minus participation in the relevant program Within-Group – observe outcomes of same students in program
and out of program (no need for controls) Between-Group – observe outcomes of different students, some of
whom participated in the program and some of whom did not (control for pre-existing group differences)
Select Comparable Cohorts
Within group comparisons Same students, compare performance in Fast-Track and non-Fast-Track
courses during same time period “Do students who earn GORs in both Fast-Track and non-Fast-Track
courses perform better, worse, or the same in the two formats?”
Between group comparisons Different students, one cohort earned a GOR in at least one Fast-Track
course and one cohort earned no GORs in a Fast-Track course across the same time period
“Do students who earn GORs in Fast-Track courses perform better, worse, or the same as students who do not earn GORs in Fast-Track courses?”
Select variables to control so that “all else is equal”
Within-Group Comparisons
1) Determine time period of interest Ensure that there are enough data to make comparisons
and that programmatic changes were not implemented during the selected period
Chaffey fast-track example: Fast-track courses were first implemented in spring 2010, but
significantly increased starting fall 2011 To obtain a strong sample size and ensure that some of the kinks
were worked out, data were analyzed from fall 2011 and later Using MIS referential files, select for fall 2011 and spring 2012
terms
Within-Group Comparisons
2) Code your data file so that student behavior in and out of the program can be measured
Chaffey fast-track example: Obtain a list of all fast-track sections from course scheduler or
other party on campus
Use obtained list to flag all fast-track sections in MIS file
Search start and end dates and delete short-term sections from file (use xf02 “SESSION-DATE-BEGINNING” and xf03 “SESSION-DATE-ENDING”)
Within-Group Comparisons
Delete all cases in which a student did not earn a GOR in fall 2011 or spring 2012
Create coding system for fast-track and full-term sections (e.g., compute two new variables, fast-track = 1 if section is fast-track and full-term = 1 if section is full-term)
Aggregate number of fast-track sections and number of full-term sections by student id and term (this will give you two new variables in your dataset that reflect a count of GORs each student earned in fast-track and full-term courses for each semester)
Within-Group Comparisons
3) Select for students whose behavior reflects program participation and program non-participation across the selected time period
Chaffey fast-track example: Select cases in which the sum of fast-track GORs >= 1 and the sum
of full-term GORs >= 1 (i.e., student has taken at least one fast-track and one full-term course)
Save selected cases to a new file
Within-Group Comparisons
4) Compare performance outcomes of same students in program and out of program
77.4%
70.0% 71.3%
65.0%
70.0%
75.0%
80.0%
Fast-Track GORs
Full-Term GORs
All Fall 2011 GORs
d = .17
d = .03
d = .14
N = 55,368 N = 4,546 N = 4,153
Same students All College
Succ
ess R
ate
Between-Group Comparisons
1) Determine time period of interest Ensure that there are enough data to make comparisons
and that programmatic changes were not implemented during the selected period
Chaffey fast-track example: Fast-track courses were first implemented in spring 2010, but
significantly increased starting fall 2011 To obtain a strong sample size and ensure that some of the kinks
were worked out, data were analyzed from fall 2011 and later Using MIS referential files, select for fall 2011 and spring 2012
terms
Between-Group Comparisons
2) Code data file so that two distinct cohorts, one of which participated in the program and one of which did not participate in the program, are identified
Chaffey fast-track example: Obtain a list of all fast-track sections from course scheduler or
other party on campus
Use obtained list to flag all fast-track sections in MIS file
Aggregate number of fast-track sections by student id and term (this will give you a new variable in your dataset that reflects a count of GORs each student earned in fast-track courses for each semester)
Between-Group Comparisons
Remove all records in which a GOR was not assigned
Create cohort variable with two mutually exclusive groups Cohort 1 consists of anyone who earned a GOR in a fast-track course
during the specified term (i.e., fast-track variable >= 1)
Cohort 2 consists of anyone who earned a GOR in a course or courses other than fast-track during the specified term (i.e., fast-track variable = 0)
Between-Group Comparisons
3) Compare cohort groups on a variety of pre-existing variables to measure differences outside of program participation (these will guide you in setting up controls for the next step)
Chaffey fast-track example: Gender, Ethnicity, Age, DPS Status, Enrollment Status, Academically
Disadvantaged Status, First Generation Status, Term Units Attempted, Term Units Earned, Cumulative Units Attempted, Cumulative Units Earned, Cumulative GPA, Self-Efficacy, Assessment Scores
Example of Categorical Variable Comparisons
Background Characteristics
Fast-Track Students Non-Fast-Track Students
|d| n % n %
Gender
Female 1,402 51.9 9,560 57.1 .10
Male 1,174 43.5 6,575 39.3 .09
Unknown 123 4.6 597 3.6 .05
First Generation
Yes 596 26.3 4,007 28.1 .27
No 1,669 73.7 10,264 71.9
Example of Continuous Variable Comparisons
Academic Characteristics
Fast-Track Students (n = 2,699)
Non-Fast-Track Students (n = 16,732)
|d| M SD M SD
Term Units Att 10.08 4.61 8.50 4.33 .36
Term Units Earn 7.21 4.89 5.79 4.59 .31
Cum Units Att 31.41 26.91 31.80 27.98 .01
Cum Units Earn 28.26 24.95 28.77 26.69 .02
Cum GPA* 2.57 1.04 2.42 1.12 .14
Self-Efficacy** 5.98 .83 5.93 .84 .06
*Fast-Track Students n = 2,689, Non-Fast-Track Students n = 16,643 ** Fast-Track Students n = 1,565, Non-Fast-Track Students n = 9,408
Between-Group Comparisons
4) Note where non-programmatic differences exist between cohort 1 and cohort 2, if observed
Chaffey fast-track example: Selecting for differences of d = .25 or higher, fast-track and non-
fast-track students were different in three areas: first-generation college status, term units attempted, and term units earned
Between-Group Comparisons
5) Conduct analyses to compare cohort 1 and cohort 2 performance outcomes, controlling for observed pre-existing differences between groups
Chaffey fast-track example: Calculate a partial correlation to measure the relationship
between cohort group and course success, while “controlling” for the effects of first generation status and units attempted (not units completed because it is too highly correlated with units attempted)
Between-Group Comparisons
Zero-Order r Partial r Effect Size
|d|
Cohort Group .01 .00 .02
Term Units Attempted* .06 .00 .12
First-Generation Status* -.03 -.03 .06
*p < .01
Correlates of Course Success among Students Earning a GOR in Fall 2011 (N = 19,431)
Cohort Comparison Conclusions
Students who earned at least one GOR each in fast-track and full-term courses in fall 2011 demonstrated statistically significantly higher course success rates in fast-track courses than in full-term courses. These findings, however, were not determined to be practically significant because of the large sample sizes and small effect size values.
Students who earned at least one GOR in a fast-track course in fall 2011 demonstrated course success rates that were not statistically significantly or practically different from course success rates of students who did not earn any GORs in fast-track courses in fall 2011.
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