Hostname: page-component-5f745c7db-nzk4m Total loading time: 0 Render date: 2025-01-06T21:12:40.864Z Has data issue: true hasContentIssue false
  • English
  • Français

Comparing the Variances of Dependent Groups

Published online by Cambridge University Press:  01 January 2025

Rand R. Wilcox
Rand R. Wilcox*
Affiliation:
University of Southern California
*
Send requests for reprints to Dr. Rand R. Wilcox, Dept of Psychology, University of Southern California, Los Angeles, CA 90089-1061
Get access Rights & Permissions [Opens in a new window]

Abstract

Recently several new attempts have been made to find a robust method for comparing the variances of J dependent random variables. However, empirical studies have shown that all of these procedures can give unsatisfactory results. This paper examines several new procedures that are derived heuristically. One of these procedures was found to perform better than all of the robust procedures studied here, and so it is recommended for general use.

Keywords

bootstrapmediantrimmed meansigned rank test
Type
Original Paper
Information
Psychometrika , Volume 54 , Issue 2 , June 1989 , pp. 305 - 315
Copyright
Copyright © 1989 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

The author would like to thank the reviewers for their very helpful comments on an earlier draft of this paper.

References

Box, G. E. P. (1953). Nonormality and tests on variances. Biometrika, 40, 318–335.CrossRefGoogle Scholar
Bradley, J. V. (1980). Nonrobustness in Z, t, and F tests at large samples. Bulletin of the Psychonomic Society, 16, 333–336.CrossRefGoogle Scholar
Brown, M. B., Forsythe, A. B. (1974). Robust tests for the equality of variances. Journal of the American Statistical Association, 69, 364–367.CrossRefGoogle Scholar
Choi, S. C., Wette, R. (1972). A test for the homogeneity of variances among correlated variables. Biometrics, 28, 589–592.CrossRefGoogle Scholar
Cohen, A. (1986). Comparing variances of correlated variables. Psychometrika, 51, 379–391.CrossRefGoogle Scholar
Conover, W. J., Johnson, M. E., Johnson, M. M. (1981). A comparative study of tests for homogeneity of variances with applications to the outer continental shelf bidding data. Technometrics, 23, 351–361.CrossRefGoogle Scholar
Fleishman, A. I. (1978). A method for simulating non-normal distributions. Psychometrika, 43, 521–532.CrossRefGoogle Scholar
Friedman, M. (1937). The use of ranks to avoid the assumption of normality implicit in the analysis of variance. Journal of American Statistical Association, 32, 675–701.CrossRefGoogle Scholar
Han, C. P. (1968). Testing the homogeneity of a set of correlated variances. Biometrika, 55, 317–326.CrossRefGoogle Scholar
Han, C. P. (1969). Testing the homogeneity of variances in a two-way classification. Biometrics, 25, 153–158.CrossRefGoogle Scholar
Harris, P. (1985). Testing for variance homogeneity of correlated variables. Biometrika, 72, 103–107.CrossRefGoogle Scholar
Huynh, H., Feldt, L. (1976). Estimation of the Box correction for degrees of freedom from sample data in randomized block and split-plot designs. Journal of Educational Statistics, 1, 69–82.CrossRefGoogle Scholar
Iman, R. L. (1974). A power study of a rank transform for the two-way classification model when interaction may be present. Canadian Journal of Statistics, 2, 227–239.CrossRefGoogle Scholar
Iman, R. L., Hora, S., Conover, W. (1984). Comparison of asymptotically distribution-free procedures for the analysis of complete blocks.. Journal of the American Statistical Association, 79, 674–685.CrossRefGoogle Scholar
IMSL. (1975). Library 1, Vol. II, Houston: Author.Google Scholar
Levy, K. J. (1976). A procedure for testing the equality of p-correlated variances. British Journal of Mathematical and Statistical Psychology, 29, 89–93.CrossRefGoogle Scholar
Lord, F., Novick, M. (1968). Statistical theories of mental test scores, Reading, MA: Addison-Wesley.Google Scholar
Miller, R. G. (1968). Jackknifing variances. Annals of Mathematical Statistics, 39, 567–582.CrossRefGoogle Scholar
Morgan, W. A. (1939). A test for the significance of the difference between the two variances in a sample from a normal bivariate population. Biomerika, 31, 13–19.Google Scholar
Man, E. J. C. (1939). A note normal correlation. Biometrika, 31, 9–12.Google Scholar
Quade, D. (1979). Using weighted rankings in the analysis of complete blocks with additive block effects. Journal of the American Statistical Association, 74, 680–683.CrossRefGoogle Scholar
Sandvik, L., Olsson, B. (1982). A nearly distribution-free test for comparing dispersion in [aired samples. Biometrika, 69, 484–485.CrossRefGoogle Scholar