Killeen's probability of replication and predictive probabilities: how to compute, use, and interpret them.

P. R. Killeen's (2005a) probability of replication (prep) of an experimental result is the fiducial Bayesian predictive probability of finding a same-sign effect in a replication of an experiment. prep is now routinely reported in Psychological Science and has also begun to appear in other journals. However, there is little concrete, practical guidance for use of prep, and the procedure has not received the scrutiny that it deserves. Furthermore, only a solution that assumes a known variance has been implemented. A practical problem with prep is identified: In many articles, prep appears to be incorrectly computed, due to the confusion between 1-tailed and 2-tailed p values. Experimental findings reveal the risk of misinterpreting prep as the predictive probability of finding a same-sign and significant effect in a replication (p srep). Conceptual and practical guidelines are given to avoid these pitfalls. They include an extension to the case of unknown variance. Moreover, other uses of fiducial Bayesian predictive probabilities for analyzing, designing ("how many subjects?"), and monitoring ("when to stop?") experiments are presented. Concluding remarks emphasize the role of predictive procedures in statistical methodology.