Solution Manual for Experimental Design: Procedures for the Behavioral Sciences , 4th Edition

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Solutions Manual for
Experimental
Design
Procedures for
the Behavioral
Sciences
Roger E.
Kirk

iii
C O N T E N T S
Chapter 1 Research Strategies and the Control of Nuisance Variables 1
Chapter 2 Experimental Design : An Overview 3
Chapter 3 Fundamental Assumptions in Analysis of Variance 14
Chapter 4 Completely Randomized Design 19
Chapter 5 Multiple Comparison Tests 27
Chapter 6 Trend Analysis 32
Chapter 7 General Linear Model Approach to ANOVA 41
Chapter 8 Randomized Block Designs 47
Chapter 9 Completely Randomized Factorial Design With
Two Treatments 54
Chapter 10 Completely Randomized Factorial Design With
Three or More Treatments and Randomized Block
Factorial Design 61
Chapter 11 Hierarchical Designs 68
Chapter 12 Split-Plot Factorial Designs: Design With
Group-Treatment Confounding 77
Chapter 13 Analysis of Covariance 86
Chapter 14 Latin Square and Related Designs 90
Chapter 15 Confounded Factorial Designs: Designs With
Group-Interaction Confounding 94
Chapter 16 Fractional Factorial Designs: Designs With Treatment-
Interaction Confounding 101

1
C H A P T E R 1
Research Strategies
and the Control of
Nuisance Variables
2. c. EU is a student; OU is a student.
d. EU is a rat; OU is a rat.
e. EU is a telephone number; OU is a respondent.
3. c. Unacceptable d. Acceptable
4. c. (i) Amount of flurazepam (ii) Hypnotic suggestibility (iii) Gender, previous
hypnotic experience
d. (i) Three fixed ratio schedules of reinforcement (ii) Key pecking rate (iii) Age
of pigeons, phase of estrous cycle
6. a. In an experiment, subjects are randomly assigned to the independent variable; in a
quasi-experiment, subjects are not randomly assigned to the independent variable.
b. Subjects were not randomly assigned to independent variable, which was adding or not
adding fluoride to the water.
7. a. Obtain a sample of n children. For each child, randomize the order of presenting the
three types of televised violence with the restriction that each type of violence is
presented first, second, and third an equal number of times.
b. Use a hidden camera to videotape children in a familiar environment as they watch
television and note their facial expressions when various forms of violence are
depicted.
8. e. Retrospective cohort study. The study involved a nonexperimental research strategy in
which the subjects were classified on the basis of their earlier earnings during a six-
month period. Multiple dependent variables were investigated, and these variables also
occurred prior the beginning of the study.
f. Retrospective cohort study. The study involved a nonexperimental research strategy in
which the subjects were classified on the basis of the independent variable, which was
appearing or not appearing in the juvenile court in Houston, TX.
g. Time-lag study. The study involved a nonexperimental research strategy in which the

Chapter 1 Research Strategies and the Control of Nuisance Variables
2
dependent variable was measured at three different times on three different groups of
cohorts.
h. Retrospective cohort study. The study involved a nonexperimental research strategy in
which university records were used to identify students who were first-born, second-
born, and so on, and their recreational activities.
i. Prospective study. The study involved a nonexperimental research strategy in which the
independent and dependent variables were observed after the onset of the investigation.
j. Retrospective cohort study. The study involved a nonexperimental research strategy in
which men were identified who had or had not been exposed to chemicals used as fire
retardants. The two samples of men were subsequently compared in terms of primary
thyroid dysfunction.
9. c. History, compensatory rivalry by respondents receiving less desirable treatments,
resentful demoralization of respondents receiving less desirable treatments
d. Selection, selection-history effects
e. Selection, selection-history effects, mortality
f. History, selection, selection-history effects, mortality
10. c. Interaction of selection and treatment
d. Interaction of selection and treatment
11. b. b, d, f, i
c. b, d, f, i
12. a. Subjects were randomly sampled; residence was held constant. The age of the subjects
was restricted.
c. The city and gender of the drivers were held constant; age of the drivers and the length
of time that they had driven a cab were restricted.
d. The students within a matched pair were randomly assigned to the programs; the grade
level was held constant.
f. The sample from the Houston, TX, court was obtained by random sampling; the gender
of the subjects was held constant.
g. The gender of the subjects was held constant.
h. The gender of the subjects and the university that they attended were held constant.
j. The gender of the subjects and the city in which they worked were held constant.

3
C H A P T E R 2
Experimental Designs:
An Oveview
2. d. (i) RB-3 design (ii) H0 : μ.1 = μ.2 = μ.3 (iii) Y ij = μ + αj + πi + εij (i = 1, . . . ,
14; j = 1, . . . , 3)
e. (i) t test for dependent samples (ii) H0 : μ.1 ≤ μ.2 , where μ.1 and μ.2 denote the
population means for English-Canadian and French-Canadian students, respectively.
(iii) Y ij = μ + αj + πi + εij (i = 1, . . . , 50; j = 1, 2)
f. (i) CRF-62 design (ii) H0 : μ1. = μ2. = . . . = μ6. ; H0 : μ.1 = μ.2 ; H0 : μ jk – μ j !k
– μ !j k + μ !j !k = 0 for all j and k (iii) Y ijk = μ + αj + βk + (αβ)jk + εi(jk) (i = 1, . . . ,
50; j = 1, . . . , 6; k = 1, 2)
g. (i) CR-3 design (ii) H0 : μ1 = μ2 = μ3 (iii) Y ij = μ + αj + εi(j) (i = 1, . . . , 30; j
= 1, . . . , 3)
3. a. The grand mean is the average value around which the treatment means vary.
b. A treatment effect is the deviation of the grand mean from a treatment mean.
c. An error effect is all effects not attributable to a treatment level or treatment
combination.
4. b. A completely randomized design is the simplest design to lay out and analyze. The
randomization procedures for the randomized block and Latin square designs are more
complex than those for the completely randomized design, but the latter designs enable
a researcher to isolate the effects of one nuisance variable or, in the case of the Latin
square design, two nuisance variables.
5. c. a1b1 , a1b2 , a1b3 , a2b1 , a2b2 , a2b3 , a3b1 , a3b2 , a3b3
d. a1b1 , a1b2 , a2b1 , a2b2 , a3b1 , a3b2 , a4b1 , a4b2
e. a1b1c1 , a1b1c2 , a1b2c1 , a1b2c2 , a2b1c1 , a2b1c2 , a2b2c1 , a2b2c2 , a3b1c1 , a3b1c2 , a3b2c1 ,
a3b2c2

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Chapter 2 Experimental Designs: An Overview
4
6. d. CR-5 design with n = 6
Treat.
Level
Dep.
Var.
Group1
!
"
#
Subject1
!
Subject6
a1
!
a1
Y11
!
Y61
Y.1
Group2
!
"
#
Subject1
!
Subject6
a2
!
a2
Y12
!
Y62
Y.2
Group3
!
"
#
Subject1
!
Subject6
a3
!
a3
Y13
!
Y63
Y.3
Group4
!
"
#
Subject1
!
Subject6
a4
!
a4
Y14
!
Y64
Y.4
Group5
!
"
#
Subject1
!
Subject6
a5
!
a5
Y15
!
Y65
Y.5
e. t test for dependent samples with n = 7
Treat.
Level
Dep.
Var.
Treat.
Level
Dep.
Var.
Block 1
Block 2
Block 3
!
Block 7
a1
a1
a1
!
a1
Y11
Y21
Y31
!
Y71
a2
a2
a2
!
a2
Y12
Y22
Y32
!
Y7 2
Y.1
Y.2

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Chapter 2 Experimental Designs: An Overview
5
f. RB-4 design with n = 6
Treat.
Level
Dep.
Var.
Treat.
Level
Dep.
Var.
Treat.
Level
Dep.
Var.
Treat.
Level
Dep.
Var.
Block 1
Block 2
Block 3
!
Block 6
a1
a1
a1
!
a1
Y11
Y21
Y31
!
Y61
a2
a2
a2
!
a2
Y12
Y22
Y32
!
Y62
a3
a3
a3
!
a3
Y13
Y23
Y33
!
Y63
a4
a4
a4
!
a4
Y14
Y24
Y34
!
Y64
Y1.
Y2.
Y3.
!
Y6.
Y.1
Y.2
Y.3
Y.4
g. CRF-222 design with n = 3
Treat.
Comb.
Dep.
Var.
Group1
!
"
#
$
#
Subject1
Subject2
Subject3
a1b1c1
a1b1c1
a1b1c1
Y1111
Y2111
Y3111
Y.111
Group2
!
"
#
$
#
Subject1
Subject2
Subject3
a1b1c2
a1b1c2
a1b1c2
Y1112
Y2112
Y3112
Y.112
Group3
!
"
#
$
#
Subject1
Subject2
Subject3
a1b2c1
a1b2c1
a1b2c1
Y1121
Y2121
Y3121
Y.121
! ! !
Group8
!
"
#
$
#
Subject1
Subject2
Subject3
a2b2c2
a2b2c2
a2b2c2
Y1222
Y2222
Y3222
Y.222

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Chapter 2 Experimental Designs: An Overview
6
h. LS-3 design with n = 3
Treat.
Comb.
Dep.
Var.
Group1
!
"
#
$
#
Subject1
Subject2
Subject3
a1b1c1
a1b1c1
a1b1c1
Y1111
Y2111
Y3111
Y.111
Group2
!
"
#
$
#
Subject1
Subject2
Subject3
a1b2c3
a1b2c3
a1b2c3
Y1123
Y2123
Y3123
Y.123
Group3
!
"
#
$
#
Subject1
Subject2
Subject3
a1b3c2
a1b3c2
a1b3c2
Y1132
Y2132
Y3132
Y.132
Group4
!
"
#
$
#
Subject1
Subject2
Subject3
a2b1c2
a2b1c2
a2b1c2
Y1212
Y2212
Y3212
Y.212
! ! !
Group9
!
"
#
$
#
Subject1
Subject2
Subject3
a3b3c1
a3b3c1
a3b3c1
Y1331
Y2331
Y3331
Y.331

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Chapter 2 Experimental Designs: An Overview
7
8. d. RB-3 design with n = 14
Treat.
Level
Dep.
Var.
Treat.
Level
Dep.
Var.
Treat.
Level
Dep.
Var.
Block 1
Block 2
Block 3
!
Block 14
a1
a1
a1
!
a1
Y11
Y21
Y31
!
Y14, 1
a2
a2
a2
!
a2
Y12
Y22
Y32
!
Y14, 2
a3
a3
a3
!
a3
Y13
Y23
Y33
!
Y14, 3
Y1.
Y2.
Y3.
!
Y14.
Y.1
Y.2
Y.3
e. t test for dependent samples with n1 and n2 = 50
Treat.
Level
Dep.
Var.
Treat.
Level
Dep.
Var.
Block 1
Block 2
Block 3
!
Block 50
a1
a1
a1
!
a1
Y11
Y21
Y31
!
Y50, 1
a2
a2
a2
!
a2
Y12
Y22
Y32
!
Y50, 2
Y.1
Y.2

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Chapter 2 Experimental Designs: An Overview
9
g. CR-3 design with n = 30
Treat.
Level
Dep.
Var.
Group1
!
"
#
$#
Animal1
!
Animal30
a1
!
a1
Y11
!
Y30, 1
Y.1
Group2
!
"
#
$#
Animal1
!
Animal30
a2
!
a2
Y12
!
Y30, 2
Y.2
Group3
!
"
#
$#
Animal1
!
Animal30
a3
!
a3
Y13
!
Y30, 3
Y.3
9. a.
b. As the number of hours of deprivation increases, the difference in running time among
the three reinforcement conditions decreases.
12. a. A scientific hypothesis is a testable supposition that is tentatively adopted to account
for certain facts and to guide in the investigation of others. A statistical hypothesis is a
statement about one or more parameters of a population or the functional form of a
population.
b. (i) Alternative hypothesis (ii) Null hypothesis
15. a. State the null and alternative hypotheses—H0 : μ = 45, H1 : μ ≠ 45. Specify the test
statistic—t = (Y ! μ0 ) / ( ˆ" / n ) . Specify the sample size—n = 27, and the sampling
distribution—t distribution. Specify the level of significance—α = .05. Obtain random
1a
2a
1b 2b 3b
4
5
6
7
8
9
a3
Running time (sec.)
10 hrs. 15 hrs. 20 hrs.
Hours of deprivation
1a 2a
1b
2b
3b
4
5
6
7
8
9
a3
Running time (sec.)
Small Medium Large
Magnitude of reinforcement

Loading page 12...

Chapter 2 Experimental Designs: An Overview
10
samples of size n = 27, compute t, and make a decision.
b. Reject the null hypothesis if t falls in either the lower or upper 2.5% of the sampling
distribution of t; otherwise, do not reject the null hypothesis. If the null hypothesis is
rejected, conclude that the mean for children in the experimental program is not equal
to the mean for ninth-graders who have been observed during the past several years; if
the null hypothesis is not rejected, do not draw this conclusion.
c.
d. t = Y ! μ0
ˆ" / n = 52.5 ! 45.0
15 / 27 = 7.5
2.89 = 2.60 , p = .015.
The population mean for children in the experimental program was not equal to the
mean for ninth-graders who have been observed during the past several years. The
difference between children who did or did not participate in the experimental program,
52.5 versus 45.0, was statistically significant, t(26) = 2.60, p = .015.
e.
d = 52.5 ! 45 / 15 = 0.5 ; this is a medium size effect.
f. Y ! t.05/2, 26 ˆ"
n < μ < Y + t.05/2, 26 ˆ"
n
52.5 ! 2.056(15)
27 < μ < 52.5 + 2.056(15)
27
46.6 < μ < 58.4
The researcher can be 95% confident that μ is greater than 46.6 or less than 58.4. The
null hypothesis is not tenable.
g. Y.05 = μ0 + t.05/2, 26 ˆ!
n = 45 + 2.056(15)
27 = 50.935
t = Y.05 ! "μ
ˆ# / n = 50.935 ! 52.5
15 / 27 = !1.565
2.887 = !0.54
TDIS(0.54,26,1) =.30 = ˆ! ; 1 – ˆ! =.70
Critical region
! = .025
Don't reject H0
H0
Reject
t
Critical region
! = .025
H0
Reject
f (t)

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Chapter 2 Experimental Designs: An Overview
11
h.
True Situation
μ = 45 !μ = 52.5
Researcher’s
μ = 45
Correct acceptance
1 – α = 1 – .05
= .95
Type II error
ˆ! = .30
Decision
μ ≠ 45
Type I error
α = .05
Correct rejection
1 – ˆ! = 1 – .30
= .70
16. c. Correct rejection d. Correct acceptance
e. Correct rejection f. Type I error
17. The power of an experiment can be increased by (1) adopting a lower level of
significance, (2) increasing the size of the sample, (3) refining the experimental
methodology so as to decrease the size of the population standard deviation, and (4)
increasing the magnitude of the treatment effects considered worth detecting.
Increasing the sample size is often the simplest way to increase power. The other ways
of increasing power may lead to problems or may not be feasible. For example, the
adoption of α > .05 may preclude the publication of the research. Refining the
experimental methodology so as to decrease the size of the population standard
deviation may be prohibitively expensive. Increasing the magnitude of the treatment
effects considered worth detecting may not be appropriate.
18. a. State the null and alternative hypotheses—H0 : μ1 – μ2 ≤ 0, H1 : μ1 – μ2 > 0. Specify the
test statistic— t = (Y.1 ! Y.2 ) / ˆ"Pooled
2 1
n1
+ 1
n2
#
$
%
&
'
( . Specify the sample size—n1 = 24, n2
= 23, and the sampling distribution—t distribution. Specify the level of significance—α
= .05. Randomly assign N = 47 subjects to the two game types, compute t, and make a
decision.
b. Reject the null hypothesis if t falls in the upper 5% of the sampling distribution of t;
otherwise, do not reject the null hypothesis. If the null hypothesis is rejected, conclude
that the risk-related cognitions of men who play racing video games is higher than that
for the men who play the neutral games; if the null hypothesis is not rejected, do not
draw this conclusion.

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Chapter 2 Experimental Designs: An Overview
12
c.
d. !Pooled
2 = (
n1 " 1)!1
2 + (
n 2 " 1)!2
2
(
n1 " 1) + (
n 2 " 1) = (24 " 1)(1.3) 2 + (23" 1)(1.2) 2
(24 " 1) + (23" 1) = 1.568
t = (Y.1 ! Y.2 ) / ˆ"Pooled
2 1
n1
+ 1
n2
#
$
%
&
'
( = (7.54 ! 6.41) / 1.568 1
24 + 1
23
"
#$
%
&'
= 1.13 / 0.365 = 3.09 . The p value is less than .002.
The mean risk-related cognitions for men who played the racing video games was
higher than that for the men who played the neutral games. The difference between the
means, 7.54 versus 6.41, was statistically significant, t(45) = 3.09, p < .002.
e. g = Y.1 ! Y.2 / ˆ"Pooled = 7.54 ! 6.41 / 1.25 = 0.90 ; this is a large effect.
f. (Y.1 ! Y.2 ) ! t.05,45 ˆ"Pooled
2 1
n1
+ 1
n2
#
$
%
&
'
( < μ1 ! μ2
(7.54 ! 6.41) ! 1.679 1.568 1
24 + 1
23
"
#$
%
&' < μ1 ! μ2
0.52 < μ 1 – μ 2
The researcher can be 95% confident that μ 1 – μ 2 is greater than 0.52. The null
hypothesis is not tenable.
g. Y.05 = !0 + t.05,45 ˆ"Pooled
2 1
n1
+ 1
n2
#
$
%
&
'
( = 0 + 1.679 1.568 1
24 + 1
23
!
"#
$
%& = 0.613
t = Y.05 ! "#0
ˆ$Pooled
2 1
n1
+ 1
n2
%
&
'
(
)
*
= 0.613 ! 1.0
1.568 1
24 + 1
23
"
#$
%
&'
= !0.387
0.365 = !1.06
TDIS(1.06,45,1) =.15 = ˆ! ; 1 – ˆ! =.85
Critical region
! = .05
Don't reject H0
H0
Reject
t
f(t)

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