# A Five-Decision Testing Procedure to Infer the Value of a Unidimensional Parameter

## Details

Serval ID

serval:BIB_B3F330DFF316

Type

**Article**: article from journal or magazin.

Collection

Publications

Institution

Title

A Five-Decision Testing Procedure to Infer the Value of a Unidimensional Parameter

Journal

The American Statistician

ISSN

0003-1305

1537-2731

1537-2731

Publication state

Published

Issued date

02/10/2019

Volume

73

Number

4

Pages

321-326

Language

english

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.

Keywords

Statistics, Probability and Uncertainty, Statistics and Probability, General Mathematics

Web of science

Funding(s)

Swiss National Science Foundation / 31003A-143914

Create date

04/01/2020 12:39

Last modification date

15/07/2020 5:26