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

316 CHAPTER 10 | The t Test for Two Independent Samples
LEARNING CHECK
1. A researcher obtains an independent-measures t statistic of t = 2.38 for a study
comparing two treatments with a sample of n = 14 in each treatment. What is the
correct decision for a regular two-tailed hypothesis test?
a. Reject the null hypothesis with α = .05 but not with α = .01.
b. Reject the null hypothesis with α = .05 or with α = .01.
c. Reject the null hypothesis with α = .01 but not with α = .05.
d. Fail to reject the null hypothesis with either alpha level.
2. A researcher study comparing performance for males and females predicts that
females will have higher scores. If a one-tailed test is used to evaluate the results,
then what is the correct statement for the alternative hypothesis (H 1
)?
a. μ females
> μ males
b. μ females
≥ μ males
c. μ females
< μ males
d. μ females
≤ μ males
3. A researcher is using an F max
test to evaluate the homogeneity of variance assumption
and an independent-measures t test with pooled variance to evaluate the mean difference
between two treatment conditions. What are the preferred outcomes for the two tests?
a. Reject H 0
for both.
b. Fail to reject H 0
for both.
c. Reject H 0
for F max
but fail to reject H 0
for the t test.
d. Fail to reject H 0
for F max
but reject H 0
for the t test.
ANSWERS
1. A, 2. A, 3. D
10.4 Effect Size and Confidence Intervals
for the Independent-Measures t
LEARNING OBJECTIVES
9. Measure effect size for an independent-measures t test using either Cohen’s d or r 2 ,
the percentage of variance accounted for.
10. Use the data from two separate samples to compute a confidence interval describing
the size of the mean difference between two treatment conditions or two populations.
11. Describe the relationship between a hypothesis test with an independent-measures
t statistic using α = .05 and the corresponding 95% confidence interval for the mean
difference.
12. Describe how the results of an independent-measures t test and measures of effect
size are reported in the scientific literature.
As noted in Chapters 8 and 9, a hypothesis test is usually accompanied by a report of effect
size to provide an indication of the absolute magnitude of the treatment effect. One technique
for measuring effect size is Cohen’s d, which produces a standardized measure of
mean difference. In its general form, Cohen’s d is defined as
d 5
mean difference
standard deviation 5 m 2m 1 2
s