How and Why Alpha Should Depend on Sample Size: A Bayesian-Frequentist Compromise for Significance Testing

Abstract

In management research, fixed alpha levels in statistical testing are ubiquitous. However, in highly powered studies, they can lead to Lindley’s paradox, a situation where the null hypothesis is rejected despite evidence in the test actually supporting it. We propose a sample-size-dependent alpha level that combines the benefits of both frequentist and Bayesian statistics, enabling strict hypothesis testing with known error rates while also quantifying the evidence for a hypothesis. We offer actionable guidelines of how to implement the sample-size-dependent alpha in practice and provide an R-package and web app to implement our method for regression models. By using this approach, researchers can avoid mindless defaults and instead justify alpha as a function of sample size, thus improving the reliability of statistical analysis in management research.