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Section 16.2 Summary of Inference for Relative Risk
| RV \ EV |
\(Group 1\) |
\(Group 2\) |
| \(Success\) |
\(A\) |
\(B\) |
| \(Failure\) |
\(C\) |
\(D\) |
| \(Total\) |
\(A + C\) |
\(B + D\) |
Relative Risk Procedures.
Statistic: Ratio of conditional proportions (typically set up to be larger than one) =
\(\frac{\hat{p}_1}{\hat{p}_2}\)
Hypotheses: \(H_0\!: \frac{\pi_1}{\pi_2} = 1\text{;}\) \(H_a\!: \frac{\pi_1}{\pi_2} < 1\text{,}\) \(\frac{\pi_1}{\pi_2} > 1\text{,}\) or
\(\frac{\pi_1}{\pi_2} \neq 1\)
p-value: Fisher’s Exact Test or normal approximation on
\(\ln\left(\frac{\hat{p}_1}{\hat{p}_2}\right)\)
Confidence interval for \(\frac{\pi_1}{\pi_2}\text{:}\) Exponentiate endpoints of
\begin{equation*}
\ln\left(\frac{\hat{p}_1}{\hat{p}_2}\right) \pm z^*\sqrt{\frac{1}{A}-\frac{1}{A+C}+\frac{1}{B}-\frac{1}{B+D}}
\end{equation*}
See the
Technology Detour for instructions on simulating random assignment for two-way tables.
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