The assessment of replication success based on relative effect size

TL;DR

This paper refines a reverse-Bayes method for assessing replication success by focusing on relative effect size, introducing the golden level for more accurate and consistent conclusions in replication studies.

Contribution

It proposes a new recalibration of replication success assessment based on relative effect size, improving power and error control over standard significance-based methods.

Findings

The golden level ensures replication success only if the replication effect exceeds the original.

The approach controls Type-I error rate with larger or equal sample sizes in replication.

Application to large datasets shows more appropriate inferences and penalizes effect shrinkage.

Abstract

Replication studies are increasingly conducted in order to confirm original findings. However, there is no established standard how to assess replication success and in practice many different approaches are used. The purpose of this paper is to refine and extend a recently proposed reverse-Bayes approach for the analysis of replication studies. We show how this method is directly related to the relative effect size, the ratio of the replication to the original effect estimate. This perspective leads to a new proposal to recalibrate the assessment of replication success, the golden level. The recalibration ensures that for borderline significant original studies replication success can only be achieved if the replication effect estimate is larger than the original one. Conditional power for replication success can then take any desired value if the original study is significant and the replication sample size is large enough. Compared to the standard approach to require statistical significance of both the original and replication study, replication success at the golden level offers uniform gains in project power and controls the Type-I error rate if the replication sample size is not smaller than the original one. An application to data from four large replication projects shows that the new approach leads to more appropriate inferences, as it penalizes shrinkage of the replication estimate compared to the original one, while ensuring that both effect estimates are sufficiently convincing on their own.