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

582 CHAPTER 17 | The Chi-Square Statistic: Tests for Goodness of Fit and Independence
LEARNING CHECK
1. If a chi-square test for goodness of fit has df = 1 then the individuals are classified
into ___ categories and if a chi-square test for independence has df = 1 then the
individuals are classified into ___ categories.
a. 2, 2
b. 2, 4
c. 1, 4
d. 1, 1
2. A sample of 100 people is classified by gender (male/female) and by whether or
not they are registered voters. The sample consists of 60 females, of whom 50 are
registered voters, and 40 males, of whom 25 are registered voters. If these data were
used for a chi-square test for independence, the expected frequency for registered
males would be ______.
a. 15
b. 25
c. 30
d. 45
3. A chi-square test for independence is conducted for data from a 2 × 2 data matrix
with a total of n = 40 participants. If the data produce χ 2 = 4.00, then what decision
should be made?
a. Reject H 0
with α = 0.5 but not with α = .01.
b. Reject H 0
with α = 0.1 but not with α = .05.
c. Reject H 0
with either α = 0.5 or α = .01.
d. Fail to reject H 0
with α = 0.5 or with α = .01.
ANSWERS
1. B, 2. C, 3. A
17.4 Effect Size and Assumptions for the Chi-Square Tests
LEARNING OBJECTIVES
9. Compute Cohen’s w to measure effect size for both chi-square tests.
10. Compute the phi-coefficient or Cramér’s V to measure effect size for the chi-square
test for independence.
11. Identify the basic assumptions and restrictions for chi-square tests.
■ Cohen’s w
Hypothesis tests, like the chi-square test for goodness of fit or for independence, evaluate
the statistical significance of the results from a research study. Specifically, the intent of
the test is to determine whether it is likely that the patterns or relationships observed in the
sample data could have occurred without any corresponding patterns or relationships in
the population. Tests of significance are influenced not only by the size or strength of the
treatment effects but also by the size of the samples. As a result, even a small effect can be
statistically significant if it is observed in a very large sample. Because a significant effect