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.