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

Jan De Neve (UGent) and Olivier Thas (UGent)
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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, INTUITIVE NONPARAMETRIC APPROACH, PROBABILISTIC INDEX, RANK-TESTS, CONFIDENCE-INTERVALS, 2-WAY LAYOUTS, HYPOTHESES, STATISTICS, SIZE, TRANSFORM, MEDICINE

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Citation

Please use this url to cite or link to this publication:

Chicago
De Neve, Jan, and Olivier Thas. 2017. “A Mann-Whitney Type Effect Measure of Interaction for Factorial Designs.” Communications in Statistics-theory and Methods 46 (22): 11243–11260.
APA
De Neve, Jan, & Thas, O. (2017). A Mann-Whitney type effect measure of interaction for factorial designs. COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 46(22), 11243–11260.
Vancouver
1.
De Neve J, Thas O. A Mann-Whitney type effect measure of interaction for factorial designs. COMMUNICATIONS IN STATISTICS-THEORY AND METHODS. 2017;46(22):11243–60.
MLA
De Neve, Jan, and Olivier Thas. “A Mann-Whitney Type Effect Measure of Interaction for Factorial Designs.” COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 46.22 (2017): 11243–11260. Print.
@article{8161041,
  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.},
  author       = {De Neve, Jan and Thas, Olivier},
  issn         = {0361-0926},
  journal      = {COMMUNICATIONS IN STATISTICS-THEORY AND METHODS},
  language     = {eng},
  number       = {22},
  pages        = {11243--11260},
  title        = {A Mann-Whitney type effect measure of interaction for factorial designs},
  url          = {http://dx.doi.org/10.1080/03610926.2016.1263739},
  volume       = {46},
  year         = {2017},
}

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