Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

676 APPENDIX C | Solutions for Odd-Numbered Problems in the Text
Fail to reject H 0
. There are no significant differences
among the three treatments.
b. In problem 18 the individual differences were
relatively large and consistent. When the
individual differences were subtracted out,
the error was greatly reduced.
21. The null hypothesis states that there are no differences
among the three weeks. With df = 2, 15, the critical
value is 3.68.
Source SS df MS
Between Treatments 12 2 6 F(2, 15) = 0.90
Within Treatments 100 15 6.67
Total 112 17
Fail to reject H 0
. There are no significant differences
among the three weeks. For these data, η 2 = 12
112 =
0.107.
23. a. The null hypothesis states that there are no differences
between treatments, H 0
: μ 1
= μ 2
= μ 3
. For
an independent-measures design, the critical value
is 3.88.
Source SS df MS
Between Treatments 40 2 20.00 F(2, 12) = 3.24
Within Treatments 74 12 6.17
Total 114 14
b. The null hypothesis states that there are no
differences between treatments, H 0
: μ 1
= μ 2
= μ 3
.
For a repeated-measures design, the critical value
is 4.46.
Source SS df MS
Between Treatments 40 2 20.0 F(2, 8) = 8.00
Within Treatments 74 12
Between Subjects 54 4
Error 20 8 2.5
Total 114 14
c. The independent measures design includes all the
individual differences in the error term (MS within
).
25. a.
As a result the F-ratio, F(2,12) = 3.24 is not
significant. With a repeated measures design, the
individual differences are removed and the result
is a significant F-ratio, F(2,8) = 8.00, p < .05.
Source SS df MS
Between Treatments 40.5 1 40.5 F(1, 8) = 20.25
Within Treatments 38 16
Between Subjects 22 8
Error 16 8 2
Total 78.5 17
The F-ratio has df = 1, 8 and the critical value is 5.32.
Reject H 0
. There is a significant difference between the
two tattoo conditions.
b. For the t test, the mean difference is M D
= 3,
SS for the difference scores is 32, the variance is
3
4, and the standard error is 0.667. t = 0.667 = 4.50.
With df = 8, the critical value is 2.306. Reject H 0
.
There is a significant difference between the two
tattoo conditions. Note that F = t 2 .
27. a. The null hypothesis states that there is no difference
between the two treatments, H 0
: μ D
= 0. The
critical region consists of t values beyond ±3.182.
The mean difference is M D
= 4.5. The variance for
the difference scores is 9, the estimated standard
error is 1.50, and t(3) = 3.00. Fail to reject H 0
.
b. The null hypothesis states that there is no
difference between treatments, H 0
: μ 1
= μ 2
.
The critical value is F = 10.13.
Source SS df MS
Between Treatments 40.5 1 40.5 F(1, 3) = 9.00
Within Treatments 31 6
Between Subjects 17.5 3
Error 13.5 3 4.5
Total 71.5 7
Fail to reject H 0
. Note that F = t 2 .
CHAPTER 14 Two-Factor ANOVA
1. a. In analysis of variance, an independent variable (or a
quasi-independent variable) is called a factor.
b. The values of a factor that are used to create the
different groups or treatment conditions are called
the levels of the factor.
c. A research study with two independent (or quasiindependent)
variables is called a two-factor study.
3. During the second stage of the two-factor ANOVA
the mean differences between treatments are analyzed
into differences from each of the two main effects and
differences from the interaction.
5. a. M = 5
b. M = 1
c. M = 9