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

SECTION 17.3 | The Chi-Square Test for Independence 579
TABLE 17.7
Degrees of freedom and
expected frequencies. (Once
three values have been
selected, all the remaining
expected frequencies are
determined by the row totals
and the column totals. This
example has only three free
choices, so df = 3.)
Red Yellow Green Blue
25 5 10 ? 50
? ? ? ? 150
100 20 40 40
The following example is an opportunity to test your understanding of the expected frequencies
and the df value for the chi-square test for independence.
EXAMPLE 17.3
A researcher would like to know which factors are most important to people who are buying
a new car. A sample of n = 200 customers between the ages of 20 and 29 are asked
to identify the most important factor in the decision process: Performance, Reliability, or
Style. The researcher would like to know whether there is a difference between the factors
identified by women compared to those identified by men. The data are as follows:
Observed Frequencies of Most Important
Factor According to Gender
Male
Female
Performance Reliability Style Totals
21 33 26 80
19 67 34 120
Totals 40 100 60
Compute the expected frequencies and determine the value for df for the chi-square test.
You should find expected frequencies of 16, 40, and 24 for the males and 24, 60, and 36 for
the females. df = 2.
■
■ An Example of the Chi-Square Test for Indepenedence
The following example demonstrates the complete hypothesis-testing procedure for the
chi-square test for independence.
EXAMPLE 17.4
Many parents allow their underage children to drink alcohol in limited situations when
an adult is present to supervise. The idea is that teens will learn responsible drinking
habits if they first experience alcohol in a controlled environment. Other parents take
a strict no-drinking approach with the idea that they are sending a clear message about
what is right and what is wrong. Recent research, however, suggests that the more
permissive approach may actually result in more negative consequences (McMorris
et al., 2011). In the study, teens who were allowed to drink with their parents were
significantly more likely to experienced alcohol-related problems than teens who were
not allowed to drink. In an attempt to replicate this study, researchers surveyed a sample
of 150 students each year from ages 14–17. The students were asked about their alcohol
use and about alcohol-related problems such as binge drinking, fights, and blackouts.
The results are shown in Table 17.8. Do the data show a significant relationship between
the parents’ rules about alcohol and subsequent alcohol-related problems?