174 Chapter 6 Categorical Data and Chi-Square
information on the gender of the students and the college (within the university) in which
they were enrolled.
a. Use any statistical package to tabulate Gender against College.
b. What is the chi-square test on the hypothesis that College enrollment is independent of
Gender?
c. Interpret the results.
6.35 When we look at the variables in Mireault’s data, we will want to be sure that there are not
systematic differences of which we are ignorant. For example, if we found that the gender
of the parent who died was an important variable in explaining some outcome variable, we
would not like to later discover that the gender of the parent who died was in some way re-
lated to the gender of the subject, and that the effects of the two variables were confounded.
a. Run a chi-square test on these two variables.
b. Interpret the results.
c. What would it mean to our interpretation of the relationship between gender of the par-
ent and some other variable (e.g., subject’s level of depression) if the gender of the par-
ent is itself related to the gender of the subject?
6.36 Zuckerman, Hodgins, Zuckerman, and Rosenthal (1993) surveyed over 500 people and
asked a number of questions on statistical issues. In one question a reviewer warned a re-
searcher that she had a high probability of a Type I error because she had a small sample
size. The researcher disagreed. Subjects were asked, “Was the researcher correct?” The pro-
portions of respondents, partitioned among students, assistant professors, associate profes-
sors, and full professors, who sided with the researcher and the total number of respondents
in each category were as follows:
Assistant Associate Full
Students Professors Professors Professors
Proportion .59 .34 .43 .51
Sample size 17 175 134 182(Note: These data mean that 59% of the 17 students who responded sided with the
researcher. When you calculate the actual obtained frequencies, round to the nearest
whole person.)
a. Would you agree with the reviewer, or with the researcher? Why?
b. What is the error in logic of the person you disagreed with in (a)?
c. How would you set up this problem to be suitable for a chi-square test?
d. What do these data tell you about differences among groups of respondents?
6.37 The Zuckerman et al. paper referred to in the previous question hypothesized that faculty
were less accurate than students because they have a tendency to give negative responses to
such questions. (“There must be a trick.”) How would you design a study to test such a
hypothesis?
6.38 Hout, Duncan, and Sobel (1987) reported data on the relative sexual satisfaction of married
couples. They asked each member of 91 married couples to rate the degree to which they