Aspirin and Heart Attack (Physicians' Health Study)
Reviewed by the crosstabs.com methods team · Last updated
In this table, treatment is significantly associated with myocardial infarction — a negligible association: χ²(1, N = 22071) = 25.01, p < .001, V = .03.
The data
| Treatment \ Myocardial infarction | Heart attack | No heart attack | Total |
|---|---|---|---|
| Aspirin | 104 | 10,933 | 11,037 |
| Placebo | 189 | 10,845 | 11,034 |
| Total | 293 | 21,778 | 22,071 |
Background
The Physicians' Health Study was a randomized, double-blind, placebo-controlled trial that enrolled 22,071 US male physicians to test whether low-dose aspirin (325 mg every other day) prevents cardiovascular disease. The aspirin arm was stopped early, in 1988, because the answer was already clear.
This table cross-tabulates treatment assignment against whether the participant suffered a myocardial infarction during follow-up: 104 heart attacks among 11,037 physicians on aspirin versus 189 among 11,034 on placebo — roughly a 44% reduction in risk.
The example is a favorite in statistics courses because it shows how a large sample can make a small absolute difference (about 0.9% versus 1.7%) decisively significant. The chi-square p-value is tiny while Cramér's V is, by conventional labels, negligible — both statements are true, and reporting them together is the honest summary.
Results
Chi-square test
χ² = 25.01
df = 1, p < .001
Effect size
Cramér's V = 0.034
a negligible association
Fisher's exact test
p < .001
two-sided, exact for this 2×2 table
Odds ratio
OR = 0.55
95% CI [0.43, 0.69]
APA-style report: χ²(1, N = 22071) = 25.01, p < .001, V = .03. N = 22,071.
Interpretation
The chi-square test rejects independence at the conventional 0.05 level (p < .001): a pattern this strong is unlikely if treatment and myocardial infarctionwere unrelated. Cramér's V of 0.034 puts this in the negligible range — the association, while it may be statistically detectable, is trivially weak in practical terms.
Because this is a 2×2 table, Fisher's exact test (p < .001) provides an exact significance check, and the odds ratio of 0.55 (95% CI [0.43, 0.69]) summarizes the strength of the relationship in odds terms.
Caveats
- Statistical significance and practical importance diverge here: with N over 22,000, even a small absolute risk difference yields a very small p-value while the effect size (Cramér's V) stays tiny. In a clinical context, relative and absolute risk reductions communicate the result better than V.
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