A Model-Averaging Approach to Replication: The Case of prep

The purpose of the recently proposed p(rep) statistic is to estimate the probability of concurrence, that is, the probability that a replicate experiment yields an effect of the same sign (Killeen, 2005a). The influential journal Psychological Science endorses p(rep) and recommends its use over that of traditional methods. Here we show that p(rep) overestimates the probability of concurrence. This is because p(rep) was derived under the assumption that all effect sizes in the population are equally likely a priori. In many situations, however, it is advisable also to entertain a null hypothesis of no or approximately no effect. We show how the posterior probability of the null hypothesis is sensitive to a priori considerations and to the evidence provided by the data; and the higher the posterior probability of the null hypothesis, the smaller the probability of concurrence: When the null hypothesis and the alternative hypothesis are equally likely a priori, p(rep) may overestimate the probability of concurrence by 30% and more. We conclude that p(rep) provides an upper bound on the probability of concurrence, a bound that brings with it the danger of having researchers believe that their experimental effects are much more reliable than they actually are.