When to adjust alpha during multiple testing: A consideration of disjunction, conjunction, and individual testing

TL;DR

This paper clarifies when alpha adjustments are appropriate during multiple hypothesis testing, emphasizing their suitability for disjunction testing but not for conjunction or individual testing, to improve scientific validity.

Contribution

It distinguishes three types of multiple testing and specifies the conditions under which alpha adjustment is appropriate, addressing a common misconception in research practices.

Findings

Alpha adjustment is suitable for disjunction testing.

Alpha adjustment is inappropriate for conjunction testing.

Alpha adjustment should not be automatically applied in all multiple testing scenarios.

Abstract

Scientists often adjust their significance threshold (alpha level) during null hypothesis significance testing in order to take into account multiple testing and multiple comparisons. This alpha adjustment has become particularly relevant in the context of the replication crisis in science. The present article considers the conditions in which this alpha adjustment is appropriate and the conditions in which it is inappropriate. A distinction is drawn between three types of multiple testing: disjunction testing, conjunction testing, and individual testing. It is argued that alpha adjustment is only appropriate in the case of disjunction testing, in which at least one test result must be significant in order to reject the associated joint null hypothesis. Alpha adjustment is inappropriate in the case of conjunction testing, in which all relevant results must be significant in order to reject the joint null hypothesis. Alpha adjustment is also inappropriate in the case of individual testing, in which each individual result must be significant in order to reject each associated individual null hypothesis. The conditions under which each of these three types of multiple testing is warranted are examined. It is concluded that researchers should not automatically (mindlessly) assume that alpha adjustment is necessary during multiple testing. Illustrations are provided in relation to joint studywise hypotheses and joint multiway ANOVAwise hypotheses.