Section 13.6 Choice of Procedures for Comparing Two Proportions
| Study design | Two binary variables, but not case-control study | Two binary variables, but not case-control study | Two binary variables |
|---|---|---|---|
| Parameter | Difference in population proportions (\(\pi_1 - \pi_2\)) | Relative Risk (\(\pi_1/\pi_2\)) | Odds Ratio (\(\tau\)) |
| Null Hypothesis | \(H_0:\) \(\pi_1 - \pi_2 = 0\) | \(H_0:\) \(\pi_1/\pi_2 = 1\) | \(H_0:\) \(\tau = 1\) |
| Simulation | Independent random sampling from binomial processes; Random assignment with hypergeometric distribution | ||
| Exact p-value | Fisher’s Exact Test | ||
| Can use \(z\) procedures if | At least 5 successes and 5 failures in each group | ||
| Confidence interval | \(\hat{p}_1 - \hat{p}_2 \pm z^*\sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1} + \frac{\hat{p}_2(1-\hat{p}_2)}{n_2}}\) | exp of [ln(\(\hat{p}_1/\hat{p}_2\)) ± \(z^*\sqrt{\frac{1}{A}-\frac{1}{A+C}+\frac{1}{B}-\frac{1}{B+D}}\)] | exp of [ln(\(AD/BC\)) ± \(z^*\sqrt{\frac{1}{A}+\frac{1}{B}+\frac{1}{C}+\frac{1}{D}}\)] |
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