Figure 1: Basis for sample size formulae. Shown in a lighter colour, and with the usual orientation, is the sampling distribution of the test statistic under the null scenario. Shown in the darker colour, and upside down to distinguish its landmarks more easily, is the sampling distribution under the alternative (nonnull) scenario. Although they are in this instance, the standard errors under the null and alternative will not necessarily be equal. The two distributions are separated by an amount Δ, the difference in the (comparative) parameter of interest. For a 2-sided test with a false positive rate of a to have at least 100(1- β) power against a non-zero difference Δ, the two absolute distances Za/2SEnull and ZβSEalt must sum to less than Δ. In this example, a= 0:05 (so that Zα/2= 1:96) and (1-β) = 0.8 (so that Zβ= -0:84).