A New Standard for the Analysis and Design of Replication Studies

Leonhard Held

A new standard is proposed for the evidential assessment of replication studies. The approach combines a specific reverse-Bayes technique with prior-predictive tail probabilities to define replication success. The method gives rise to a quantitative measure for replication  success, called the sceptical p-value. The sceptical p-value integrates  traditional significance of both the original and replication study with a comparison of the respective effect sizes. It incorporates the uncertainty of both the original and replication effect estimates and reduces to the ordinary p value of the replication study if the uncertainty  of the original effect estimate is ignored. The proposed framework can  also be used to determine the power or the required sample size to achieve replication success. Numerical calculations highlight the difficulty to achieve replication success if the evidence from the original study is only suggestive. An application to data from the Open Science Collaboration project on the replicability of psychological  science illustrates the proposed methodology.

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