172 Chapter 6 Categorical Data and Chi-Square
Chi-Square Tests
Asymp. Sig.
Value df (2-sided)
Pearson Chi-Square 37.229a 2 .000
Likelihood Ratio 29.104 2 .000
N of Valid Cases 634
a0 cells (.0%) have expected count less than 5. The minimum expected count is 8.59.Symmetric Measures
Approx.
Value Sig.
Nominal by Phi .242 .000
Nominal Cramer’s V .242 .000
Contingency Coefficient .236 .000
N of Valid Cases 634Exhibit 6.2 (continued)6.24 A more complete set of data on heart attacks and aspirin, from which Table 6.10 was taken,
is shown below. Here we distinguish not just between Heart Attacks and No Heart Attacks,
but also between Fatal and Nonfatal attacks.
Myocardial InfarctionFatal Attack NonFatal Attack No Attack Total
Placebo 18 171 10,845 11,034
Aspirin 5 99 10,933 11,037
Total 23 270 21,778 22,071a. Calculate both Pearson’s chi-square and the likelihood ratio chi-square table. Interpret
the results
b. Using only the data for the first two columns (those subjects with heart attacks), calcu-
late both Pearson’s chi-square and the likelihood ratio chi-square and interpret your
results.
c. Combine the Fatal and Nonfatal heart attack columns and compare the combined col-
umn against the No Attack column, using both Pearson’s and likelihood ratio chi-
squares. Interpret these results.
d. Sum the Pearson chi-squares in (b) and (c) and then the likelihood ratio chi-squares in
(b) and (c), and compare each of these results to the results in (a). What do they tell you
about the partitioning of chi-square?
e. What do these results tell you about the relationship between aspirin and heart attacks?
6.25 Calculate and interpret Cramér’s Vand useful odds ratios for the results in Exercise 6.24.
6.26 Compute the odds ratio for the data in Exercise 6.10. What does this value mean?
6.27 Compute the odds ratio for Table 6.4 What does this ratio add to your understanding of the
phenomenon being studied?