Justify Your Alpha: A Primer on Two Practical Approaches

Abstract

The default use of an alpha level of.05 is suboptimal for two reasons. First, decisions based on data can be made more efficiently by choosing an alpha level that minimizes the combined Type 1 and Type 2 error rate. Second, it is possible that in studies with very high statistical power, p values lower than the alpha level can be more likely when the null hypothesis is true than when the alternative hypothesis is true (i.e., Lindley’s paradox). In this article, we explain two approaches that can be used to justify a better choice of an alpha level than relying on the default threshold of.05. The first approach is based on the idea to either minimize or balance Type 1 and Type 2 error rates. The second approach lowers the alpha level as a function of the sample size to prevent Lindley’s paradox. An R package and Shiny app are provided to perform the required calculations. Both approaches have their limitations (e.g., the challenge of specifying relative costs and priors) but can offer an improvement to current practices, especially when sample sizes are large. The use of alpha levels that are better justified should improve statistical inferences and can increase the efficiency and informativeness of scientific research.