Equivalence of the statistics for replicability and area under the ROC curve.

Two statistics, one recent and one well known, are shown to be equivalent. The recent statistic, p(rep), gives the probability that the sign of an experimental effect is replicable by an experiment of equal power. That statistic is equivalent to the well-known measure for the area under a receiver operating characteristic (ROC) curve for statistical power against significance level. Both statistics can be seen as exemplifying the area theorem of psychophysics.