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Robust Techniques for Testing Heterogeneity of Variance Effects in Factorial Designs

Published online by Cambridge University Press:  01 January 2025

Ralph G. O’Brien
Ralph G. O’Brien*
Affiliation:
University of Virginia
*
Requests for reprints should be sent to Ralph G. O’Brien, Department of Psychology, Gilmer Hall, University of Virginia, Charlottesville, Virginia, 22901.
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Abstract

Several ways of using the traditional analysis of variance to test heterogeneity of spread in factorial designs with equal or unequal n are compared using both theoretical and Monte Carlo results. Two types of spread variables, (1) the jackknife pseudovalues of s2 and (2) the absolute deviations from the cell median, are shown to be robust and relatively powerful. These variables seem to be generally superior to the Z-variance and Box-Scheffé procedures.

Keywords

variance testinghomogeneity of varianceanalysis of variancejackknifedispersion
Type
Original Paper
Information
Psychometrika , Volume 43 , Issue 3 , September 1978 , pp. 327 - 342
Copyright
Copyright © 1978 The Psychometric Society

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Footnotes

This research was sponsored by Public Health Service Training Grant MH-08258 from the National Institute of Mental Health. The author thanks Mark I. Appelbaum, Elliot M. Cramer, and Scott E. Maxwell for their helpful criticisms of this paper. An earlier version of this work was presented at the Annual Meeting of the Psychometric Society, Murray Hill, New Jersey, April, 1976.

References

Appelbaum, M. I., & Cramer, E. M. Some problems in the nonorthogonal analysis of variance. Psychological Bulletin, 1974, 81, 335–347.CrossRefGoogle Scholar
Basu, J. P., Odell, P. L., & Lewis, T. O. The effects of intraclass correlation on certain significance tests when sampling from multivariate normal population. Communications in Statistics, 1974, 3, 899–908.Google Scholar
Box, G. E. P., & Andersen, S. L. Permutation theory in the derivation of robust criteria and the study of departures from assumption. Journal of the Royal Statistical Society, Series B, 1955, 17, 1–26.CrossRefGoogle Scholar
Brown, M. B., & Forsythe, A. B. Robust tests for equality of variances. Journal of the American Statistical Association, 1974, 69, 364–367.CrossRefGoogle Scholar
Games, P. A., Winkler, H. R., & Probert, D. A. Robust tests for homogeneity of variance. Educational and Psychological Measurement, 1972, 32, 887–909.CrossRefGoogle Scholar
Gartside, P. S. A study of methods for comparing several variances. Journal of the American Statistical Association, 1972, 67, 342–346.CrossRefGoogle Scholar
Glass, G. V., Peckham, P. D., & Sanders, J. R. Consequences of failure to meet assumptions underlying the fixed effects analyses of variance and covariance. Review of Educational Research, 1972, 42, 237–288.CrossRefGoogle Scholar
Gray, H. L., & Schucany, W. R. The generalized jackknife statistic, 1972, New York: Marcel Dekker.Google Scholar
Hays, W. L. Statistics for the social sciences, 2nd ed., New York: Holt, Rinehart, & Winston, 1973.Google Scholar
Kendall, M. G., & Stuart, A. The advanced theory of statistics, 3rd ed., London: Charles Griffin, 1969.Google Scholar
Layard, M. W. J. Robust large sample tests for homogeneity of variances. Journal of the American Statistical Association, 1973, 68, 195–198.CrossRefGoogle Scholar
Levene, H. Robust tests for the equality of variances. In Olkin, I., Ghurye, S. G., Hoeffding, W., Madow, W. G., & Mann, H. B. (Eds.), Contributions to probability and statistics, 1960, Palo Alto: Stanford University Press.Google Scholar
Levy, K. J. An empirical comparison of the Z-variance and Box-Scheffé tests for homogeneity of variance. Psychometrika, 1975, 40, 519–524.CrossRefGoogle Scholar
Marsaglia, G., & Bray, T. A. One-line random number generators and their use in combinations. Communications of the ACM, 1968, 11, 757–759.CrossRefGoogle Scholar
Martin, C. G. Comment on Levy's “An empirical comparison of the Z-variance and Box-Scheffé tests for homogeneity of variance. Psychometrika, 1976, 41, 551–556.CrossRefGoogle Scholar
Miller, R. G. Jr. Jackknifing variances. Annals of Mathematical Statistics, 1968, 39, 567–582.CrossRefGoogle Scholar
Miller, R. G. Jr. The jackknife—a review. Biometrika, 1974, 61, 1–15.Google Scholar
Mosteller, F., & Tukey, J. W. Data analysis, including statistics. In Lindzey, G. & Aronson, E. (Eds.), The handbook of social psychology, 2nd ed., Reading, Mass.: Addison-Wesley, 1968.Google Scholar
O'Brien, R. G. Factorial designs for the analysis of spread. (Doctoral dissertation, University of North Carolina, 1975). Dissertation Abstracts International, 1976, 37, 1328B. (University Microfilms No. 76-20,062)Google Scholar
Overall, J. E., & Woodward, J. A. A simple test for heterogeneity of variance in complex factorial designs. Psychometrika, 1974, 39, 311–318.CrossRefGoogle Scholar
Scheffé, H. A. The analysis of variance, 1959, New York: Wiley.Google Scholar
Zelen, M. Factorial experiments in life testing. Technometrics, 1959, 1, 269–288.CrossRefGoogle Scholar
Zelen, M. Analysis of two-factor classifications with respect to life tests. In Olkin, I., Ghurye, S. G., Hoeffding, W., Madow, W. G., & Mann, H. B. (Eds.), Contributions to probability and statistics, 1960, Palo Alto: Stanford University Press.Google Scholar
Walsh, J. E. Concerning the effect of intraclass correlation on certain significant tests. Annals of Mathematical Statistics, 1947, 18, 88–96.CrossRefGoogle Scholar