Description
1. Table 1 is from a report on the relationship between aspirin use and myocardial infarction (heart attacks) by
the Physicians’ Health Study Research Group at Harvard Medical School. Find the p-value for testing that
Myocardial Infarction
Group Yes No
Placebo 158 10410
Aspirin 71 10321
Table 1: Heart Attack Data
the incidence of heart attacks is independent of aspirin intake using the chi-square test. Interpret your results.
2. An analysis of campus accident data was made to determine the distribution of numbers of fatal accidents
for automobiles of two sizes. The data for 16 accidents are given in Table 2. Do the data indicate that the
frequency of fatal accidents is independent of the size of automobiles? Choose a test, justify your choice,
Size of auto
Small Large Total
Fatal 1 7 8
not Fatal 5 3 8
Total 6 10 16
Table 2: Campus Accident Data
perform it and interpret the results.
3. Table 3 is based on records of accidents in 1988 compiled by the Department of Highway Safety and Motor
Vehicles in Florida.
Injury
Safety Equipment in Use Fatal Non-fatal
None 1598 162526
Seat belt 502 421360
Table 3: Highway Safety Data
(a) Find and interpret the difference of proportions, relative risk, and odds ratio. Why are the relative risk
and odds ratio approximately equal?
(b) Construct 95% confidence intervals for the difference of proportions; the relative risk and the odds ratio.
Interpret.
1 STAT 4006
Religious Beliefs
Highest Degree Fundamentalist Moderate Liberal
Less than high school 178 183 108
High school of junior college 570 648 442
Bachelor or graduate 138 252 252
Table 4: Religious Belief Data
4. Table 4, from a recent General Social Survey, cross-classifies the degree of fundamentalism of subjects’ religious
beliefs by their highest degree of education.
(a) Find and interpret a measure of association between subjects’ religious beliefs and their education level.
(b) Test the independence of the religious beliefs and the degree using two-sided test with α = 0.05. (Hint:
use scores for Highest degree 1, 2, 3, and scores for religious belief 1, 2, 3.)
(c) What is the advantage for the test method we adopted in part (b), compared with the X2 and G2
tests?
5. Give a “real world” example of three variables X, Y , and Z, for which you expect X and Y to be marginally
associated but conditionally independent, controlling for Z.
6. The following table refers to applicants to graduate school at the University of California, Berkeley for the
fall 1973 session. Admissions decisions are presented by gender of applicant, for the three largest graduate
departments. Denote the three variables by A = whether admitted, G = gender, and D = department.
Whether Admitted
Male Female
Department Yes No Yes No
1 478 302 80 23
2 365 199 16 7
3 117 203 204 385
4 133 276 127 250
5 50 138 94 299
6 22 351 24 317
Table 5: Berkeley Data
(a) Find the sample AG conditional odds ratios, and compare them with the sample AG marginal odds
ratio. Why are they so different?
(b) Conduct the Cochran-Mantel-Haenszel test. Specify the hypothesis and interpret. Comment on the
applicability of this data to this data.
(c) Calculate and interpret an estimate of the common AG conditional odds ratio.
THE END
2 STAT 4006
