6533b7cefe1ef96bd1257bd7
RESEARCH PRODUCT
Rejection odds and rejection ratios: A proposal for statistical practice in testing hypotheses
Maria J. BayarriJames O. BergerDaniel J. BenjaminThomas Sellkesubject
Bayes' ruleFOS: Computer and information sciencesComputer sciencemedia_common.quotation_subjectBayesian probabilityBayesian01 natural sciencesArticle050105 experimental psychologyStatistical powerOddsMethodology (stat.ME)010104 statistics & probabilityFrequentist inferenceBayes factorsEconometrics0501 psychology and cognitive sciencesp-value0101 mathematicsFrequentistPsychology(all)General PsychologyStatistics - Methodologymedia_commonMathematicsStatistical hypothesis testingApplied Mathematics05 social sciencesBayes factorSurpriseOddsNull hypothesisType I and type II errorsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-06-01 | Journal of Mathematical Psychology |