Toward Replicability With Confidence Intervals for the Exceedance Probability

Abstract

Several scientific fields including psychology are undergoing a replication crisis. There are many reasons for this problem, one of which is a misuse of p-values. There are several alternatives to p-values, and in this article we describe a complement that is geared toward replication. In particular, we focus on confidence intervals for the probability that a parameter estimate will exceed a specified value in an exact replication study. These intervals convey uncertainty in a way that p-values and standard confidence intervals do not, and can help researchers to draw sounder scientific conclusions. After briefly reviewing background on p-values and a few alternatives, we describe our approach and provide examples with simulated and real data. For linear models, we also describe how confidence intervals for the exceedance probability are related to p-values and confidence intervals for parameters.

Keywords:

• Bayes factors
• p-values
• Psychology
• Reproducibility probability

Supplementary material

The R package exceedProb implements confidence intervals for the exceedance probability and is available on the CRAN. Results from coverage probability simulations can be found in online supplementary material, and all code for reproducing examples and simulations is available at https://github.com/bdsegal/code-for-exceedance-paper.

Acknowledgments

I would like to thank Michael R. Elliott and Peter D. Hoff for their very insightful feedback and suggestions, Somnath Sarkar and Sandra Griffith for helpful discussions, and the editor, associate editor, and reviewers for their constructive comments which greatly improved the article.