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The assessment of replicability using the sum of p -values.

Leonhard HeldSamuel PawelCharlotte Micheloud
Published in: Royal Society open science (2024)
Statistical significance of both the original and the replication study is a commonly used criterion to assess replication attempts, also known as the two-trials rule in drug development. However, replication studies are sometimes conducted although the original study is non-significant, in which case Type-I error rate control across both studies is no longer guaranteed. We propose an alternative method to assess replicability using the sum of p -values from the two studies. The approach provides a combined p -value and can be calibrated to control the overall Type-I error rate at the same level as the two-trials rule but allows for replication success even if the original study is non-significant. The unweighted version requires a less restrictive level of significance at replication if the original study is already convincing which facilitates sample size reductions of up to 10%. Downweighting the original study accounts for possible bias and requires a more stringent significance level and larger sample sizes at replication. Data from four large-scale replication projects are used to illustrate and compare the proposed method with the two-trials rule, meta-analysis and Fisher's combination method.
Keyphrases
  • machine learning
  • quality improvement