Choosing the Level of Significance: A Decision-Theoretic Approach
53 Pages Posted: 30 Aug 2015 Last revised: 6 Apr 2019
Date Written: April 5, 2019
In many areas of science including business disciplines, statistical decisions are often made almost exclusively at a conventional level of significance. Serious concerns have been raised that this contributes to a range of ill-practices such as p-hacking and data-mining that undermine research credibility. In this paper, we present a decision-theoretic approach to choosing the optimal level of significance, with a consideration of the key factors of hypothesis testing, including sample size, prior belief, and losses from Type I and II errors. We present the method in the context of testing for linear restrictions in the linear regression model. From the empirical applications in accounting, economics, and finance, we find that the decisions made at the optimal significance levels are more sensible and unambiguous than those at a conventional level, providing inferential outcomes consistent with estimation results, descriptive analysis, and economic reasoning. Computational resources are provided with two R packages.
Keywords: Bootstrapping, Expected Loss, Statistical Significance, Power Analysis
JEL Classification: A20, C12, B41
Suggested Citation: Suggested Citation