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Rejection Odds and Rejection Ratios: A Proposal for Statistical Practice in Testing Hypotheses

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Type
Preprint
Publication Date
Submission Date
Identifiers
arXiv ID: 1512.08552
Source
arXiv
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Abstract

Much of science is (rightly or wrongly) driven by hypothesis testing. Even in situations where the hypothesis testing paradigm is correct, the common practice of basing inferences solely on p-values has been under intense criticism for over 50 years. We propose, as an alternative, the use of the odds of a correct rejection of the null hypothesis to incorrect rejection. Both pre-experimental versions (involving the power and Type I error) and post-experimental versions (depending on the actual data) are considered. Implementations are provided that range from depending only on the p-value to consideration of full Bayesian analysis. A surprise is that all implementations -- even the full Bayesian analysis -- have complete frequentist justification. Versions of our proposal can be implemented that require only minor modifications to existing practices yet overcome some of their most severe shortcomings.

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