Introduction to Categorical Data Analysis

PROBLEMS 269
b. Find the McNemar z 2 statistic for Table A and the CMH statistic (4.9) for
Table B. Compare.
c. For Table B, show that the CMH statistic does not change if you delete pairs
from the data set in which both the case and the control had the same diet.
d. This sample size is too small for these large-sample tests. Find the exact P -
value for testing marginal homogeneity against the alternative hypothesis
of a higher incidence of colon cancer for the “high” red meat diet. (See
Problem 8.5.)
8.11 For the subject-specific model (8.4) for matched pairs,
logit[P(Yi1 = 1)] =αi + β, logit[P(Yi2 = 1)] =αi
the estimated variance for the conditional ML estimate ˆβ = log(n12/n21) of β
is (1/n12 + 1/n21). Find a 95% confidence interval for the odds ratio exp(β)
for Table 8.1 on helping the environment. Interpret.
8.12 For Table 7.3 on the student survey, viewing the table as matched triplets, you
can compare the proportion of “yes” responses among alcohol, cigarettes, and
marijuana.
a. Construct the marginal distribution for each substance, and find the three
sample proportions of “yes” responses.
b. Explain how you could represent the data with a three-way contingency
table in order to use a generalized CMH procedure (see Section 6.4.2) to
test marginal homogeneity.
8.13 Table 8.12, from the 2004 General Social Survey, reports subjects’ religious
affiliation in 2004 and at age 16, for categories (1) Protestant, (2) Catholic,
(3) Jewish, (4) None or Other.
Table 8.12. Data for Problem 8.13
Affiliation
Religious Affiliation Now
at Age 16 1 2 3 4
1 1228 39 2 158
2 100 649 1 107
3 1 0 54 9
4 73 12 4 137
Source: 2004 General Social Survey.
a. The symmetry model has deviance G 2 = 150.6 with df = 6. Use residuals
for the model [see equation (8.9)] to analyze transition patterns between
pairs of religions.