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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
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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
Fred FanningIsadore Newman
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
Fred FanningIsadore Newman
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?
4. Is there a significant difference between the slope of Control Group 1and Control Group 3 above and beyond individual differences?
5. Is there a significant niean difference between Control Group 2 andControl Group 3?
6. Is there a significant difference between the slope of Control Group 2and Control Group 3 above and beyond individual differences?
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.
4. There is no apparent slope difference between Control Group 1 andControl Group 3 above and beyond individual differences.
5. There is no apparent mean difference between Control Group 2 andControl Group 3.
6. There is no apparent slope difference between Control Group 2 andControl Group 3 above and beyond individual differences.
7. There appears to be a significant mean difference between ControlGroup 1 and Experimental Group 1 above and beyond individualdifferences.
8. Not applicable.
9. There appears to be a significant mean difference between ControlGroup 2 and Experimental Group 2 above and beyond individualdifferences.
10. Not applicable.
11. There appears to be a significant mean difference between ControlGroup 3 and Experimental Group 3 above and beyond individualdifferences.
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
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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).