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

674 APPENDIX C | Solutions for Odd-Numbered Problems in the Text
With df = 2, 21, the critical value for α = .05 is 3.47.
Fail to reject the null hypothesis.
15. With G = 60 and N = 15, SS between
= 30.
17. a. If the mean for treatment III were changed to M =
25, it would reduce the size of the mean differences
(the three means would be closer together).
This would reduce the size of MS between
and would
reduce the size of the F-ratio.
b. If the SS in treatment I were increased to
SS = 1400, it would increase the size of the variability
within treatments. This would increase
MS within
and would reduce the size
of the F-ratio.
19. a. The sample variances are 2.67, 3.33, and 6.00.
These values are much larger than the variances in
problem 18.
b. The larger variances should result in a smaller
F-ratio that is less likely to reject the null
hypothesis.
c.
Source SS df MS
Between Treatments 32 2 16 F(2, 9) = 4.00
Within Treatments 36 9 4
Total 68 11
With α = .05, the critical value is F = 4.26. Fail to
reject the null hypothesis and conclude that there are no
significant differences among the three treatments. The
F-ratio is much smaller as predicted.
21. a. Larger samples should increase the F-ratio.
Source SS df MS
Between Treatments 50 2 25 F(2, 72) = 12.50
Within Treatments 144 72 2
Total 194 74
The F-ratio is much larger than it was in problem 20.
b. Increasing the sample size should have little or no
effect on η 2 . η 2 = 50
144 = 0.258, which
is about the same as the value obtained in
problem 20.
23. If the F-ratio has df = 1, 34, then the experiment
compared only two treatments, and you could use a t
statistic to evaluate the data. The t statistic would have
df = 34.
CHAPTER 13
Repeated-Measures Anova
1. For an independent measures design, the variability
within treatments is the appropriate error term. For
repeated measures, however, you must subtract out
variability due to individual differences from the variability
within treatments to obtain a measure
of error.
3. a. A total of 48 participants is needed; four
separate samples, each with n = 12. The F-ratio
has df = 3, 44.
5.
b. One sample of n = 12 is needed. The F-ratio has
df = 3, 33.
Source SS df MS
Between Treatments 70 2 35 F(2, 8) = 28
Within Treatments 40 12
Between Subjects 30 4
Error 10 8 1.25
Total 110 14
7.
With df = 2, 8, the critical value is 4.46. Reject H 0
.
There are significant differences among the three
treatments.
Source SS df MS
Between Treatments 64 1 64 F(1, 7) = 112.28
Within Treatments 36 14
Between Subjects 32 7
Error 4 7 0.57
Total 100 15
With df = 1, 7, the critical value is 5.59. Reject H 0
.
There is a significant difference between the two
treatments.