For the vast majority of tests, the proof of the asymptotic correctness of this formula is easy to show. Almost all parametric1 statistical tests commonly utilize test statistics that are either exactly or asymptotically distributed as either Z, t, χ2, or F. These four distributions are closely related [21]. For example, Z2=χ12,tdf=c2=Fdf=1,c, limc→∞ tdf=c = Z, and limc→∞Fdf=k,c=χk2. From these relations, if one can derive EEE for the case of a normal test statistic (Z), it is easy to show that the EEE formula also is asymptotically correct for any test involving t, F, or χ2. Indeed, this approach underlies the rapid calculations offered in many canned statistical power calculation programs [8].
