The purpose of the recently proposed "p[subscript 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[subscript rep]" and recommends its use over that of traditional methods. Here we show that "p[subscript rep]" overestimates the probability of concurrence. This is because "p[subscript 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[subscript rep]" may overestimate the probability of concurrence by 30% and more. We conclude that "p[subscript 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. (Contains 4 footnotes and 2 figures.)