Proportions and differences

A large-sample Wald interval for one proportion is phat±z√[phat(1-phat)/n], using adequate successes and failures. For p1-p2 from independent samples, use difference±z√[phat1(1-phat1)/n1+phat2(1-phat2)/n2]. Wald intervals are classroom approximations and can perform poorly near 0 or 1. A pooled t interval for two means uses (mean1-mean2)±t sp√(1/n1+1/n2), when its assumptions hold.