Sample proportion ($\hat{p}=D/n$)

For independent Bernoulli observations with success probability $p$, the sample proportion is the success count divided by the sample size. It is an unbiased estimator with variance $p(1-p)/n$. It supplies the arm-specific risks in a risk ratio and the mean difference in a two-proportion comparison.

For two independent samples of Bernoulli random variables, the difference of their sample proportions estimates the difference of population probabilities. Since the samples are independent,Substitution of the sample proportions gives a standard error for a large-sample Wald confidence interval. This interval is a descriptive comparison of the specified groups; a causal effect needs further assumptions. Sparse counts and probabilities near zero or one can make the normal approximation poor. Testing equality can instead use a null-pooled estimate of the common probability for the test's standard error.