A Mann–Whitney type effect measure of interaction for factorial designs

Jan De Neve and Olivier Thas

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 22, 11243-11260

Abstract: We propose a measure for interaction for factorial designs that is formulated in terms of a probability similar to the effect size of the Mann–Whitney test. It is shown how asymptotic confidence intervals can be obtained for the effect size and how a statistical test can be constructed. We further show how the test is related to the test proposed by Bhapkar and Gore [Sankhya A, 36:261–272 (1974)]. The results of a simulation study indicate that the test has good power properties and illustrate when the asymptotic approximations are adequate. The effect size is demonstrated on an example dataset.

Date: 2017
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DOI: 10.1080/03610926.2016.1263739

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