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

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.

KEYWORDS:

• Factorial designs
• interaction
• probability of superiority
• rank test
• Wilcoxon–Mann–Whitney

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G05
• 62G10

Acknowledgments

The authors would like to thank the referees and associate editor for their constructive comments. The authors acknowledge the IAP research network P7/06 of the Belgian Government (Belgian Science Policy) and the Research Fund Flanders (FWO) research grants G020214N, V403114N, and K211116N.