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

324 CHAPTER 10 | The t Test for Two Independent Samples
With df = 16 and α = .05, this value is not in the critical region. Therefore, we fail to
reject the null hypothesis and conclude that there is no significant difference between the
two treatments. Although there is still a 5-point difference between sample means (as
in Figure 10.6), the 5-point difference is not significant with the increased variance. In
general, large sample variance can obscure any mean difference that exists in the data
and reduces the likelihood of obtaining a significant difference in a hypothesis test. ■
Finally, we should note that the problems associated with high variance often can be minimized
by transforming the original scores to ranks and then conducting an alternative statistical
analysis known as the Mann-Whitney test, which is designed specifically for ordinal
data. The Mann-Whitney test is presented in Appendix E, which also discusses the general
purpose and process of converting numerical scores into ranks. The Mann-Whitney test also
can be used if the data violate one of the assumptions for the independent-measures t test
(pp. 313–314).
LEARNING CHECK
1. Which of the following sets of data is most likely to reject the null hypothesis in a
test with the independent-measures t statistic. Assume that other factors are held
constant.
a. n = 20 and SS = 210 for both samples
b. n = 10 and SS = 210 for both samples
c. n = 20 and SS = 410 for both samples
d. n = 10 and SS = 410 for both samples
2. If other factors are held constant, what effect does increasing the sample sizes have
on the likelihood of rejecting the null hypothesis and measures of effect size for the
independent-measures t statistic?
a. Both the likelihood and measures of effect size will increase.
b. Both the likelihood and measures of effect size will decrease.
c. The likelihood of rejecting the null hypothesis increases but there will be little or
no effect on measures of effect size.
d. The likelihood of rejecting the null hypothesis decreases but there will be little or
no effect on measures of effect size.
3. If other factors are held constant, what effect does increasing the sample variance
have on the likelihood of rejecting the null hypothesis and measures of effect size
for the independent-measures t statistic?
a. Both the likelihood and measures of effect size will increase.
b. Both the likelihood and measures of effect size will decrease.
c. The likelihood of rejecting the null hypothesis increases but there will be little or
no effect on measures of effect size.
d. The likelihood of rejecting the null hypothesis decreases but there will be little or
no effect on measures of effect size.
ANSWERS
1. A, 2. C, 3. B