Detecting <i>p</i>‐Hacking

Abstract

We theoretically analyze the problem of testing for p ‐hacking based on distributions of p ‐values across multiple studies. We provide general results for when such distributions have testable restrictions (are non‐increasing) under the null of no p ‐hacking. We find novel additional testable restrictions for p ‐values based on t ‐tests. Specifically, the shape of the power functions results in both complete monotonicity as well as bounds on the distribution of p ‐values. These testable restrictions result in more powerful tests for the null hypothesis of no p ‐hacking. When there is also publication bias, our tests are joint tests for p ‐hacking and publication bias. A reanalysis of two prominent data sets shows the usefulness of our new tests.