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Probability of Directional Errors with Disordinal (Qualitative) Interaction

Published online by Cambridge University Press:  01 January 2025

Juliet Popper Shaffer
Juliet Popper Shaffer*
Affiliation:
University of California
*
Requests for reprints should be sent to Juliet P. Shaffer, Department of Statistics, University of California, Berkeley, CA 94720.
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Abstract

In a factorial design with two or more factors, there is nonzero interaction when the differences among the levels of one factor vary with levels of other factors. The interaction is disordinal or qualitative with respect to a specific factor, say A, if the difference between at least two levels of A is positive for some and negative for some levels of the other factors. Using standard methods of analysis, there is a potentially large probability of drawing incorrect conclusions about the signs of differences in the presence of disordinal interaction. The maximum probability of such incorrect conclusions, or directional errors, is derived for two-factor designs in which the factor of interest has two levels and the number of levels of the other factor varies.

Keywords

factorial designinteractiondisordinal interactionqualitative interactiondirectional errors
Type
Original Paper
Information
Psychometrika , Volume 56 , Issue 1 , March 1991 , pp. 29 - 38
Copyright
Copyright © 1991 The Psychometric Society

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References

Azzalini, R., & Cox, D. R. (1984). Two new tests associated with analysis of variance. Journal of the Royal Statistical Society, 46, 335–343.CrossRefGoogle Scholar
Berger, R. (1984). Testing for the same ordering in several groups of means. In Santner, T. J. & Tamhane, A. C. (Eds.), Design of experiments: Ranking and selection (pp. 241–249). New York: Dekker.Google Scholar
Berger, R. (1989). Uniformly more powerful tests for hypotheses concerning linear inequalities and normal means. Journal of the American Statistical Association, 84, 192–199.CrossRefGoogle Scholar
Bohrer, R., & Sheft, J. (1979). Misclassification probabilities in 23 factorial experiments. Journal of Statistical Planning and Inference, 3, 79–84.CrossRefGoogle Scholar
Cronbach, L. J., & Snow, R. E. (1977). Aptitudes and instructional methods, New York: John Wiley.Google Scholar
Fabian, V. (in press). On the problem of interactions in the analysis of variance. Journal of the American Statistical Association.Google Scholar
Gail, M., & Simon, R. (1985). Testing for qualitative interactions between treatment effects and patient subsets. Biometrics, 41, 361–372.CrossRefGoogle ScholarPubMed
Lehmann, E. L. (1966). Some concepts of dependence. Annals of Mathematical Statistics, 37, 1137–1153.CrossRefGoogle Scholar
Neyman, J. (1935). Complex experiments: Comments by Dr. Neyman on a paper by F. Yates. Journal of the Royal Statistical Society Supplement, 2, 235–242.Google Scholar
Simon, R. (1980). Patient heterogeneity in clinical trials. Cancer Treatment Reports, 64, 405–410.Google ScholarPubMed
Traxler, R. H. (1976). A snag in the history of factorial experiments. In Owen, D. B. (Eds.), On the history of statistics and probability (pp. 281–295). New York: Dekker.Google Scholar
Yates, F. (1935). Complex experiments. Journal of the Royal Statistical Society Supplement, 2, 181–223.CrossRefGoogle Scholar
Zelterman, D. On tests for qualitative interactions. Statistics and Probability Letters, 10, 59–63.CrossRefGoogle Scholar