A Five-Decision Testing Procedure to Infer the Value of a Unidimensional Parameter. Issue 4 (2nd October 2019)

• Record Type: Journal Article
• Authors: McDaid, Aaron; Kutalik, Zoltán; Rousson, Valentin
• Is Part Of: American statistician. Volume 73:Issue 4(2019)
• Page Start: 321
• Page End: 326
• Publication Date: 2019-10-02
• Subjects: Composite hypothesis -- Directional two-sided test -- Null hypothesis -- Probability of a wrong rejection -- Sample size calculation -- Statistical power -- Three-decision testing procedure; Statistics -- Periodicals; 001.42205
• DOI: 10.1080/00031305.2018.1437075
• Languages: English
• ISSNs: 0003-1305

Abstract

ABSTRACT: A statistical test can be seen as a procedure to produce a decision based on observed data, where some decisions consist of rejecting a hypothesis (yielding a significant result) and some do not, and where one controls the probability to make a wrong rejection at some prespecified significance level. Whereas traditional hypothesis testing involves only two possible decisions (to reject or not a null hypothesis), Kaiser's directional two-sided test as well as the more recently introduced testing procedure of Jones and Tukey, each equivalent to running two one-sided tests, involve three possible decisions to infer the value of a unidimensional parameter. The latter procedure assumes that a point null hypothesis is impossible (e.g., that two treatments cannot have exactly the same effect), allowing a gain of statistical power. There are, however, situations where a point hypothesis is indeed plausible, for example, when considering hypotheses derived from Einstein's theories. In this article, we introduce a five-decision rule testing procedure, equivalent to running a traditional two-sided test in addition to two one-sided tests, which combines the advantages of the testing procedures of Kaiser (no assumption on a point hypothesis being impossible) and Jones and Tukey (higher power), allowing for a nonnegligible (typically 20%) reduction of the sample size needed to reach a given statistical power to get a significant result, compared to the traditional approach.