DOCUMENT RESUME ED 090 250 TM 003 518 Fanning, Fred ...DOCUMENT RESUME ED 090 250 TM 003 518 AUTHOR...

DOCUMENT RESUME

ED 090 250 TM 003 518

AUTHOR Fanning, Fred; Newman, IsadoreTITLE The Development and Demonstration of Multiple

Regression Models for Operant ConditioningQuestions.

PUB DATE Mar 74NOTE 23p.; Paper presented at the annual meeting of the

American Educational Research Association (Chicago,Illinois, April 15-19, 1974)

EDRS PRICE MF-$0.75 HC-$1.50 PLUS POSTAGEDESCRIPTORS Attendance Patterns; Behavioral Counseling;

*Behavioral Science Research; *Behavior Change;Behavior Theories; Conditioned Response; High SchoolStudents; Hypothesis Testing; Instructional Prcgrams;*Models; *Multiple Regression Analysis; *OperantConditioning; Predictor Variables; ProgramEvaluation; Psychology; Research Design; StatisticalAnalysis; Student Behavior

ABSTRACTBased on the assumption that inferential statistics

can make the operant conditioner more sensitive to pcssiblesignificant relationships, regressions models were developed to testthe statistical significance between slopes and Y intercepts of theexperimental and control group subjects. These results were thencompared to the traditional operant conditioning eyeball techniqueanalysis. (Author)

U.S. DEPARTMENT OF HEALTH,EDUCATION A WELFARENATIONAL INSTITUTE OF

EDUCATIONTHIS DOCUMENT HAS BEEN REPROOUCEO EXACTLY AS RECEIVED FROM

(NJ THE PERSON OR ORGANIZATION ORIGINATING IT POINTS OF VIEW OR OPINIONSC) STATEO DO NOT NECESSARILY REPRESENT OFFICIAL NATIONAL INSTITUTE OF

Cr% EDUCATION POSITION OR POLICY

CaCa

THE DEVELOPMENT AND DEMONSTRATION OF MULTIPLE

REGRESSION MODELS FOR OPERANT CONDITIONING QUESTIONS

Fred FanningIsadore Newman

University of Akron

The Development and Demonstration of Multiple RegressionModels for Operant Conditioning Questions


The University of Akron

Abstract...based on the assumption that inferential statistics can makethe operant conditioner more sensitive to possible significant relation-ships, regression models were developed to test the statistical significancebetween slopes and Y intercepts of the experimental and control groupsubjects. These results were then compared to the traditional operantconditioning eyeball technique analysis.

Fred FanningThe University of AkronCollege of EducationAkron, Ohio 44325

The Development and Demonstration of Multiple RegressionModels for Operant Conditioning Questions


The University of Akron

Summarization of research in operant psychology has relied predomi-nately upon descriptive statistics. Probably the main reason inferentialstatistics has been given little attention is that early operant researchyielded such clear-cut distinctions that it was not necessary to resort totests of statistical significance. A second reason may be the lack of advicefrom statisticians regarding limitations of single subject data.

Presently, much research in operant psychology is being done in the .

natural environment outside the laboratory, as applied beharior modification.In these settings, the control of extraneous variables is more difficult toachieve. As a result, data may fail to exhibit the clear magnitude of effectsobserved in data from a laboratory manipulation. When this occurs, signi-ficant results may not be immediately obvious even though the expected trendseems to be present. When some doubt exists concerning the outcome of anexperimental manipulation using behavior modification procedures , considerationshould be given to the use of inferential statistics. A number of inferentialstatistical models are currently available that may assist the operant researcherin analyzing his data. These models are essentially specific applicationsof the generalized analysis of variance using multiple regression proceduresto partial variance.

The purpose of this paper is to develop and .demonstrate regression modelsthat may be useful to operant conditioners for statistically analyzing theirdata. A comparison will be presented between a regression approach toanswering operant conditioning questions and traditional operant analysis andinterpretations of the same data.

The research questions dealt with here are only examples of the manypossible kinds of questions which can be dealt with effectively using multipleregression procedures. Models will be developed to test the following questions:

2

1. Is there a significant mean difference between Control Group 1 andControl Group 2?

2. Is there a significant difference between the slope of Control Group 1and Control Group 2 above and beyond individual differences?

3. Is there a significant mean difference between Control Group 1 andControl Group 3?


5. Is there a significant niean difference between Control Group 2 andControl Group 3?


7. Is there a significant mean difference between Control Group 1 andExperimental Group 1 above and beyond individual differences?

8. Is there a significant second degree curvilinear relationship for ControlGroup 1 and Experimental Group 1 above and beyond a linear relationshipand any individual differences?

9. Is there a significant mean difference between Control Group 2 andExperimental Group 2 above and beyond individual differences?

10. Is there a significant second degree functional relationship for ControlGroup 2 and Experimental Group 2 above and beyond a linear relationshipand any individual differences?

11. Is the mean of Control Group 3 significantly different from the mean ofExperimental Group 3 above and beyond any individual differences?

3.

12. Is there a significant second degree functional relationship for ControlGroup 3 and Experimental Group 3 above and beyond a linear relationshipand any individual differences?

13. Is there a significant difference between the slope of Control Group 1and Experimental Group 1 above and beyond any individual differences?

14. Is there a s Liificant difference between the slope of Control Group 2and Experime .al Group 2 above and beyond any individual differences?

15. Is there a significant difference between the slope of Control Group 3and Experimental Group 3 above and beyond any individual differences?

METHOD

Subjects. The total subject group consisted of twelve male and female

students selected from a pool of names referred for chronic tardiness behavior

by the school psychologist, teachers, and counselors at Westland High School,

population 1,700, near Columbus, Ohio. Selection was made on the basis

of the highest reported frequency of tardiness behavior.

The sample included one male freshman, four male and one female

sophomores, two male and one female juniors, and three male seniors. All

subjects were white, from approximately middle class socioeconomic back

ground..

Material. The behavioral instruction program used in this design was

a modification of Hall's book (1971, Pt. II) describing the basic principles

of behavior modification.

The content of the control group instruction for both the teacher's daily

lesson plans and the course outline, was taken from the general psychology

text (Engle and Snellgrove, 1969), which students were given to use during

this instruction.

4

PROCEDURE

During the initial phase of this design, the control period, the twelve

subjects were assigned to three groups, four subjects to each group. Groups

1, 2, and 3 received a control treatment consisting of classroom instruction

in general psychology. Immediately following the control period, the four

students in Group 1 began receiving behavioral instruction treatment, consis-

ting of classroom instruction in behavioral principles and their application.

Group 2 continued receiving classroom instruction in general psychology, and

Group 3 received general psychology instruction. When a decelerating trend

in Group.l's tardiness behavior was noted, following instruction in behavioral

principles, then Group 2 began receiving instruction in beh4vioral principles,

and no longer received instruction in general psychology. When a decelerating

trend in Group 2's tardiness behavior was noted, general psychology'instruc-

tion was terminated with Group 3, and they began receiving instruction in

behavioral principles. Group 1 and 2 continued receiving behavioral instruc-

tion throughout the remainder of the four week class.

ANALYSIS

The data was analy2ed using two techniques:

(1) A multiple baseline design was used to demonstrate the effectivenessof the group instruction in behavioral principles (independent variable)on decelerating tardiness behavior (dependent variable). The multiple*baseline design used for analysis of data is illustrated in Figure 1.Further information concerning the use of this type of design can beobtained by reference to Baer, et. al., (1968); Hall, et. al. , (1970);and Hall, (1971, Pt. 1). Additional data representing the totalfrequency of tardiness for the 3 groups is illustrated in Table 1.

0 CJ

(1)

2.5

2.0

1.5

1.0

0.5 0

3.0

2.5

2.0

1.5

1.0

0.5 0

TAE EFFECTS OF BEHAVIORAL INSTRUCTION ON THE MEAN

FREQUENCY OF TARDINESS BEHAVIOR OF THREE CROUPS

w4AmitocammetnattOMMaln=

Control Grou

Experimental Group 1

4C1W

+46

4311

7.11

06,V

MC

MID

;

3.0

2.5 1<

Group 1

N = 4

2.0

1.5

1.0

0.5 0

01

2

Control Group 2

Experimental Group 2

Experimental

Control Group 3

1 <

Group 3

Fiore 1

10

11

12

13

Instructional Days

A Multiple Baseline Design

indicating the mean frequency of tardiness

behavior

to school and class for three

groups.

N = 4 in all

groups.

laagrovenowardwimer

14

15

16

17

IS

19

20

TABLE 1

TOTAL FREQUENCY OF TARDINESS BEHAVIOR TO SCHOOL AND CLASSFOR THREE GROUPS

IWeek 1 Week 2 Week 3 I Week 4

Group 1Control.

41

'Beh. Inst.

17

Control

18

Beh. Inst.

18

Beh. Inst.

6

Group 2

Control

17

Beh. Inst.

13

Control

35

Beh. Inst.

-I6

Group 3Baseline Control

1

26 31

4 ''Beh. Inst.

23

(2) Multiple regression was used to test the same hypothesis as theabove traditional method for analyzing the data (see 1 above).For an example of how the data is set up, Figure 2 presents thehypothesis and models used to test them.

EXAMPLE MODELS

Research Hypothesis 1: The control group mean (C1) is significantly higherthan the experimental group mean (E1) above andbeyond person differences (P) + E.

Model 1: Y1 v

= a0U + a 1(C1) + a

2(E 1) + a

3(P 1) + a

4(P2) + a

5(P 3) + a

6(P

4) + E

al = a2

Model 2: Y =a U + a(P1 ) + a ( P ) + a5 ( P ) + a ( P ) + E1. 0

Research Hypothesis 2: The slopes of the experimental group (D ) iselsignificantly different than the slope of the

control (D ) group above and beyond personcldifferences (P).

Model 3: Y =a0U+a

1(C

1) + a (E1) ) + a

3(D

c1) + a4 (Del) + a5(P1) + + a

6(P4) + Erro

1 .

a =a3 4

Model 4: Y =a U + a (C ) + a (E ). + a (Day) + a (P ) + + a (P ) + Error1 0 1 1 2 1 7 5 1 6 4

In this example there were four persons (P1

, P2

, P3

, and P4). During the control

condition (C1) each was measured on three consecutive days (D) The same

four persons were again measured on three consecutive days during the experi-

mental condition (E1).

co

Figure 2

Y1

=ao

U+

al (

C1)

+a2

(E_)

+ a

3(D

c)

+ a

4(D

e)

+ a

5(P

+ a

6(P

2)+

a7

(P3)

+ a

8(P

4) +

Err

or1

Pers

on 1

91

1

26

11

313

11

412

11

Pers

on 1

121

1

101

2

39

11

47

11

Pers

on 1

61

1

27

11

38

11

49

11

Pers

on 1

71

02

91

03

81

04

31

0

Pers

on 1

51

02

71

0

32

10

41

10

Pers

on 1

51

02

11

0

32

10

43

1O

.

An

exam

ple

of d

ata

set u

p.(N

=24

)

01

01(

1))

010

)0

1(1)

02

(2)

02(

2)0

2(2)

02

(2)

03 3

(3)

0(3

)

3(3)

03

0(3

)

o o 0 o o o 0 o o o 0 o

10

1(4)

10

1(4)(4

)1

01.

(4)

10

1(4)

10

2(5

)1

02

(5)

10

2(5

)1

02

(5)

10

3(6

)1

0,3

)(6)

10

'(6)

10

3(6)

10

00

?0

10

0.

00

10

00

01

.

10

00

.

o1

00

?0

01

0

00

01

.

10

00

.

01

o-

0.

00.

10

?0

00

1.

10

00

.

01

00

00

1"0

?0

00

1.

10

00

.

01

00

.0

01

0

00

01

.

10

00

?0

10

0.

00

10

.0

00

1.

The

re a

re f

our

pers

ons.

Eac

h is

mea

sure

d 5

times

,3

times

for

the

cont

rol

cond

ition

and

3 ti

mes

for

the

expe

rim

enta

l con

ditio

n.

cr)

Figu

re 2

Con

tinue

d

Whe

re:

Cl

= 1

ifSs

was

in c

ontr

ol c

ondi

tion

whe

n m

easu

red

zero

oth

erw

ise

El

= 1

ifSs

was

in e

xper

imen

tal c

ondi

tion

whe

n m

easu

red

zero

oth

erw

ise

Dc

= d

ay w

hen

mea

sure

d fo

r co

ntro

l gro

up z

ero

othe

rwis

e1

Del

= d

ay w

hen

mea

sure

d fo

r ex

peri

men

tal g

roup

zer

o ot

herw

ise

AE

rror

= Y

Y

U =

1 f

or e

ach

repl

icat

e in

the

stud

y

a0

... a

8=

par

tial r

egre

ssio

n w

eigh

ts

10

RESULTS AND DISCU3SION

Table 2 presents the results of the regression analysis testing each

of the fifteen questions. The operant analysis of these questions is

presented in Table 3. In comparing these tables one should note that there

is only disagreement on question five.

One major advantage of using the regression procedure, rather than

the traditional eyeball technique is that probability estimates can be attri-

buted to the accuracy of the statements.

Another advantage of the regressions procedure used is ability to test

the curvilinear relationships above and beyond linear ones, which is not

feasible with the eyeball technique on multiple baseline analysis. Similarily,

one cannot test to see if the slopes of the control group are significantly

different statistically.

In addition, as demonstrated in this paper we can also test to see 4f

the functional relationship of one treatment is significantly different: from the

functional relationship of some other treatment (across some area of interest).

These advantages represent only some of the additional information

which can be obtained through statistical analysis of operant data.

Tab

le 2

RE

SUL

TS

OF

RE

GR

ESS

ION

AN

AL

YSI

S

If n

If d

RE

SEA

RC

H Q

UE

STIO

NM

OD

EL

R2

Is th

ere

a si

gnif

ican

tm

ean

diff

eren

ce b

etw

een

Con

trol

Gro

up 1

and

Con

trol

Gro

up 2

?

Y1

= a

0U +

al (

01)

+ a

2(C

2) +

E

Y1

= a

0U

+ E

Full.

Res

tric

ted

.66 0

158

.05

94.2

8.0

0001

Is th

ere

a si

gnif

ican

tdi

ffer

ence

bet

wee

n th

esl

ope

of C

ontr

ol G

roup

1 an

d C

ontr

ol G

roup

2ab

ove

and

beyo

nd in

divi

dual

diff

eren

ces?

Y1

= a

0U +

al (

Dcl

) +

a2

(Dc2

) +

a3(

P1)

+ a

4(P2

)

+ a

5(P

3)+

+ a

10(P

8) +

EFu

ll_6

61

50.0

5.0

3.8

4Y

1 =

a0

U +

a12

(Dc1

+2)

+ a

13(

P1)

+ a

14(P

2)+

+ a

20(P

8) +

ER

estr

icte

d .6

6

Tab

le 2

Con

tinue

d

RE

SEA

RC

H Q

UE

STIO

NM

OD

EL

R2

If n

If d

FP

Is th

ere

a si

gnif

ican

t mea

n di

ffer

ence

bet

wee

nC

ontr

ol G

roup

1 a

nd C

ontr

ol G

roup

3?

Y1

a0U

+al

(C

1)+

a2(

C 3

)+

E

Y1

= a

0U

+ E

Full

.46

78.0

565

.71

.000

01

Res

tric

ted

0

Is th

ere

a si

gnif

ican

t dif

fere

nce

betw

een

the

slop

e of

Con

trol

Gro

up 1

and

Con

trol

Gro

up 3

abov

e an

d be

yond

indi

vidu

al d

iffe

renc

es?

Y =

a U

+a

(D)

+a2

) +

a)

+1

01

C1

2c3

1

a6(1

)4)

++

all(

P9)

++

a14

(P12

)

+ E

Full

.46

170

.05

.000

11.

0000

)a2

(P 1

)+

+a6

(P4)

Y1

= a

oU+

al(D

c l+c

++

a10

(P9

)+

a13

(P12

) +

ER

estr

icte

d .4

6

Tab

le 2

Con

tinue

d

RE

SEA

RC

HU

EST

ION

.MO

DE

LR

2If

nIf

d

Is th

ere

a si

gnif

ican

t mea

n di

ffer

ence

bet

wee

nC

ontr

ol G

roup

2 a

nd C

ontr

ol G

roup

3?

Y1

=a 0

U+

a 1(C

2)

+ a

2(C

3)

+ E

Y1

= a

OU

+ E

Full

.29

198

.05

41.4

2.0

0001

Res

tric

ted

0

Is th

ere

a si

gnif

ican

t dif

fere

nce

betw

een

the

slop

eof

Con

trol

Gro

up 2

and

Con

trol

Gro

up 3

. abo

ve a

ndbe

yond

indi

vidu

al d

iffe

renc

es?

Y =

a U

+ a

(D

) +

a (

D)

+ a

(P

) +

...1

01

c22

c33

+ a

10(P

12)

+ E

Full

.49

190

.05

.31

.57

Y =

a U

+al

) +

a(P

) +

..,.

10

11 c

2+3

1224

+ a

(P)

+ E

Res

tric

ted

.49

2031

Tab

le 2

Con

tinue

d

RE

SEA

RC

HU

EST

ION

Is th

ere

a si

gnif

ican

t mea

n di

ffer

ence

bet

wee

nC

ontr

ol G

roup

1 a

nd E

xper

imen

tal G

roup

1 a

bove

and

beyo

nd in

divi

dual

dif

fere

nces

?

Y1

= a

oU+

a1

(C1)

+ a

2(T

1)

+ a

3(p

1)

+

+a

(P )

+E

G4

MO

DE

LIf

nIf

d

Full

.56

171

.05

46.3

1.0

0001

Y1

=a 0

U+

a1

(P1)

++

a4

(P4)

+ E

Res

tric

ted

.27

Is th

ere

a si

gnif

ican

t sec

ond

degr

ee c

urvi

linea

rre

latio

nshi

p fo

r C

ontr

ol G

roup

1 a

nd E

xper

imen

tal

Gro

up 1

abo

ve a

nd b

eyon

d a

linea

r re

latio

nshi

pan

d an

y in

divi

dual

dif

fere

nces

?

Y1

= a

U +

a 1

(Dc)

+ a

(D

c+

a3

) +

a (

D)2

l0

2c

3el

4T

1

+ a

5(Pi

) +

+ a

8(P4

) +

EFu

ll.5

82

68.0

5.2

58

Y1

0U

+al

(D

c) +

a2

(D)

+ a

3(P

1)

+T

1

+ a

6(P

4) +

ER

estr

icte

d .5

7

Tab

le 2

Con

tinue

d

RE

SEA

RC

H Q

UE

STIO

NM

OD

EL

R2

If n

If d

Is th

ere

a si

gnif

ican

t mea

n di

ffer

ence

bet

wee

nC

ontr

ol G

roup

2 a

nd E

xper

imen

tal G

roup

2 a

bove

and

beyo

nd in

divi

dual

dif

fere

nces

?

Y1

= a

0U

+ a

1'(C )

+ a

2(T

2) +

a3

(P5)

+

+ a

6(P

8)

+ E

Full

.59

171

.05

17.1

7.0

001

Y1

= a

0U

fal

(P5)

+ .

. . +

a3

(P8)

+ E

Res

tric

ted

.50

Is th

ere

a si

gnif

ican

t sec

ond

degr

ee f

unct

iona

lre

latio

nshi

p fo

r C

ontr

ol G

roup

2 a

nd E

xper

imen

tal

Gro

up 2

abo

ve a

nd b

eyon

d a

linea

r re

latio

nshi

pan

d an

y in

divi

dual

dif

fere

nces

?

Y =

a U

+a

(D)

+ a

2)2

+ a

(D

) +

a (

D)2

10

1c2

2c2

3T

24

T2

+ a

5(P

5) +

. . .

+ a

8(P

8)

+ E

Y =

a U

+a

(D)

+ a

(D

) +

a (

13)

+1

01

c 22

T2

35

+ a

(P

) +

E6

8

Full

.63

268

.05

.82

.44

Res

tric

ted

.62

Tab

le 2

Con

tinue

d

RE

SEA

RC

H Q

UE

STIO

NM

OD

EL

R2

If n

If d

Is th

e m

ean

of C

ontr

ol G

roup

3 s

igni

fica

ntly

diff

eren

t fro

m th

e m

ean

of E

xper

imen

tal G

roup

3ab

ove

and

beyo

nd a

ny in

divi

dual

dif

fere

nces

?

Y =

a U

+ a

(C

) +

a (

T )

+ a

(P

) +

...

10

13

23

39

+ a

7(P

13)

+ E

Full

.42

171

.05

4.67

.03

Y =

a0

U +

a(1

3)

+...

+a4

(P12

) +

ER

estr

icte

d .3

91

19

Is th

ere

a si

gnif

ican

t sec

ond

degr

ee f

unct

iona

lre

latio

nshi

p fo

r C

ontr

ol G

roup

3 a

nd E

xper

imen

tal

Gro

up 3

abo

ve a

nd b

eyon

d a

linea

r re

latio

nshi

pan

d an

y in

divi

dual

dif

fere

nces

?

Y =

a U

+ a

(D

) +

a2

)2

+ a

(D

) +

a (

D)2

31

0c

2c

33

T3

4T

3

+ a

5(P

9)

++

a9

(P13

) +

EFu

ll.4

52

68.0

51.

18.3

1

Y =

a U

+ a

(D

) +

a2

T3

39

712

(D)

+ a

( 1

3 )

+ a

(13

)1

01

c3+

ER

estr

icte

d .4

4

Tab

le 2

Con

tinue

d

RE

SEA

RC

H Q

UE

STIO

N..M

OD

EL

R2

If n

.If

d

Is th

ere

a si

gnif

ican

t dif

fere

nce

betw

een

the

slop

e of

Con

trol

Gro

up 1

and

Exp

erim

enta

lG

roup

1 a

bove

and

bey

ond

any

indi

vidu

aldi

ffer

ence

s?

Y1

=a 0

U+

a 1(D

) +

a2

(DT

) +

a (

13)

+cl

13

1

+ a

(1)

) +

EFu

ll.5

71

70.0

58.

19.0

057

5

Y1

=a0

U+

al (

Dc

) +

a2

(P1)

+.

1+T

1

+ a

6(P

5) +

ER

estr

icte

d .5

2

Is th

ere

a si

gnif

ican

t dif

fere

nce

betw

een

the

slop

eof

con

trol

Gro

up 2

and

Exp

erim

enta

l Gro

up 2

abov

e an

d be

yond

any

indi

vidu

al d

iffe

renc

es?

Y =

a U

+al

) +

a (

D)

+ a

(p

) +

...1

o1

c22

T2

35

+ a

7(P

9)

+ E

Full

.63

170

.05

4.0

4

Y =

a U

+ a

(D

) +

a (

P )

+...

10

1c2

+T

25

2+

a5

(P8)

+ E

Res

tric

ted

.61

Tab

le 2

Con

tinue

d

RE

SEA

RC

H Q

UE

STIO

NM

OD

EL

R2

If r

iIf

dc2

(F

P

Is th

ere

a si

gnif

ican

t dif

fere

nce

betw

een

the

slop

e of

Con

trol

Gro

up 3

and

Exp

erim

enta

lG

roup

3 a

bove

and

bey

ond

any

indi

vidu

aldi

ffer

ence

s?

Y =

a U

+a

) +

a2)

+ a

(13

)1

0al

(D2

T3

31

+a7

(P12

)+

EFu

ll.4

81

70.0

57.

14.0

1

Y =

a U

+a

(D)

+ a

(P

) +

a (

P)

+ E

10

1c3

+T

29

612

3

Res

tric

ted

.43

19

Table 3

THE FIFTEEN TESTED QUESTIONS

Hypothesis Number

1. There appears to be a significant mean difference between ControlGroup 1 and Control Group 2.

2. There is no apparent slope difference between Control Group 1 andControl Group 2 above and beyond individual differences.

3. There appears to be a significant mean difference between ControlGroup 1 and Control Group 3.


5. There is no apparent mean difference between Control Group 2 andControl Group 3.


7. There appears to be a significant mean difference between ControlGroup 1 and Experimental Group 1 above and beyond individualdifferences.

8. Not applicable.


10. Not applicable.


12. Not applicable.

13. There appears to be a significant difference between the slope ofControl Group 1 and Experimental Group 1 above and beyond individualdifferences.

20

Table 3 Continued

Hypothesis Number

14. There appearsControl Groupdifference.

15. There appearsControl Groupdifferences.

to be a significant difference between2 and Experimental Group 2 above and

to be a significant difference between3 and Experimental Group 3 above and

the slope ofbeyond individual

the slope ofbeyond individual

21

REFERENCES

Baer, D. D. , Wolf, M. M. and Risley, T. R. "Some Current Dimensionsof Applied Behavior Analysis." journal of Applied Behavior Analysis,1968, 1, 91-97.

Engle, T. L. and Snellgrove, L. Psychology: Its Principles and Applications.Harcourt, Brace, and World, Inc., 1969.

Hall, R. V. Managing Behavior, Behavior Modification: The Measurementof Behavior. Part I, pp. 24. H. & H. Enterprises, Inc., P. 0. Box3342, Lawrence, Kansas 66044.

Hall, R. V. Managing Behavior, Behavior Modification: Basic Principles.Part II, H. & H. Enterprises, Inc., P. 0. Box 3342, Lawrence,Kansas 66044.

Hall, R. V., Cristler, C., Cranston, S. S. and Tucker, B. "Teachers andParents as Researchers Using Baseline Designs." Journal of AppliedBehavior Analysis, 1970, 3, 247-55.

Kelly, F. J., Beggs, D. L., McNeil, K.Research Design in the BehavioralApproach. Carbondale, Illinois:1969.

A., Eichelberger, T. and Lyon, J.Sciences: Multiple RegressionSouthern Illinois University Press,

Kelly, F. J., Newman, I. and McNeil, K. A. Suggested inferential statisticalmodels for research in behavioral modification. The Journal ofExperimental Education, (in press).

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