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*}
Technology:
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In Two-way Tables applet: Choose Relative Risk as statistic and check box for 95% CI
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fmsb::riskratio(A, B, A+C, B+D, conf.level, p.calc.by.independence = TRUE) -
In JMP: From the Contingency Analysis hot spot, choose Relative Risk
