= Sample size for comparing two proportions
{title2=$n\simeq[z_{1-\alpha/2}\sqrt{2\bar p(1-\bar p)}+z_{1-\beta}\sqrt{p_1(1-p_1)+p_0(1-p_0)}]^2/(p_1-p_0)^2$}
For equal independent binomial samples, the displayed normal-approximation size per group targets a two-sided significance level $\alpha$ and power $1-\beta$ at specified alternative rates, with $\bar p=(p_1+p_0)/2$. Its first <variance> term sets the null critical value and its second the alternative distribution. A numerical <sample size> is not determined by an effect ratio alone; power, sidedness, allocation and baseline rates must also be specified. Rare-event discreteness and clustered designs can materially change the achieved power.
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