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

580 CHAPTER 17 | The Chi-Square Statistic: Tests for Goodness of Fit and Independence
TABLE 17.8
A frequency distribution
showing experience with
alcohol-related problems
according to parents’
rules concerning underage
drinking.
STEP 1
Experience with
Alcohol-Related
Problems
No
Yes
Not Allowed to Drink 71 9 80
Allowed to Drink 89 31 120
160 40 n = 200
State the hypotheses, and select a level of significance. According to the null hypothesis, the
two variables are independent. This general hypothesis can be stated in two different ways:
Version 1
H 0
: In the general population, there is no relationship between parents’ rules for
alcohol use and the development of alcohol-related problems.
This version of H 0
emphasizes the similarity between the chi-square test and a correlation.
Version 2
H 0
: In the general population, the distribution of alcohol-related problems has the
same proportions for teenagers whose parents permit drinking and for those
whose parents do not.
The second version of H 0
emphasizes the similarity between the chi-square test and the
independent-measures t test.
The alternative hypothesis states that there is a relationship between the two variables
(version 1), or that the two distributions are different (version 2). Remember that the two
versions for the hypotheses are equivalent. The choice between them is largely determined
by how the researcher wants to describe the outcome. For example, a researcher may want
to emphasize the relationship between variables or the difference between groups.
For this test, we use α = .05.
STEP 2
STEP 3
Determine the degrees of freedom and locate the critical region. For the chi-square test for
independence,
df = (R – 1)(C – 1) = (2 – 1)(2 – 1) = 1
With df = 1 and α = .05, the critical value for chi-square is 3.84 (see Table B.8, p. 659).
Determine the expected frequencies, and compute the chi-square statistic. The following
table shows an empty matrix with the same row totals and column totals as the original
data. The expected frequencies must maintain the same row totals and column totals, and
create an ideal frequency distribution that perfectly represents the null hypothesis. Specifically,
the proportions for the group of 80 teens for whom alcohol was not allowed must be
the same as the proportions for the group of 120 who were permitted to drink.
Experience with
Alcohol-Related
Problems
No
Yes
Not Allowed to Drink 80
Allowed to Drink 120
160 40 n = 200