Abstract
Several ways of using the traditional analysis of variance to test heterogeneity of spread in factorial designs with equal or unequaln are compared using both theoretical and Monte Carlo results. Two types of spread variables, (1) the jackknife pseudovalues ofs 2 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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Appelbaum, M. I., & Cramer, E. M. Some problems in the nonorthogonal analysis of variance.Psychological Bulletin, 1974,81, 335–347.
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.
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.
Brown, M. B., & Forsythe, A. B. Robust tests for equality of variances.Journal of the American Statistical Association, 1974,69, 364–367.
Games, P. A., Winkler, H. R., & Probert, D. A. Robust tests for homogeneity of variance.Educational and Psychological Measurement, 1972,32, 887–909.
Gartside, P. S. A study of methods for comparing several variances.Journal of the American Statistical Association, 1972,67, 342–346.
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.
Gray, H. L., & Schucany, W. R.The generalized jackknife statistic. New York: Marcel Dekker, 1972.
Hays, W. L.Statistics for the social sciences (2nd ed.). New York: Holt, Rinehart, & Winston, 1973.
Kendall, M. G., & Stuart, A.The advanced theory of statistics (Vol. 1, 3rd ed.). London: Charles Griffin, 1969.
Layard, M. W. J. Robust large sample tests for homogeneity of variances.Journal of the American Statistical Association, 1973,68, 195–198.
Levene, H. Robust tests for the equality of variances. In I. Olkin, S. G. Ghurye, W. Hoeffding, W. G. Madow, & H. B. Mann (Eds.),Contributions to probability and statistics Palo Alto: Stanford University Press, 1960.
Levy, K. J. An empirical comparison of theZ-variance and Box-Scheffé tests for homogeneity of variance.Psychometrika, 1975,40, 519–524.
Marsaglia, G., & Bray, T. A. One-line random number generators and their use in combinations.Communications of the ACM, 1968,11, 757–759.
Martin, C. G. Comment on Levy's “An empirical comparison of theZ-variance and Box-Scheffé tests for homogeneity of variance.”Psychometrika, 1976,41, 551–556.
Miller, R. G., Jr. Jackknifing variances.Annals of Mathematical Statistics, 1968,39, 567–582.
Miller, R. G., Jr. The jackknife—a review.Biometrika, 1974,61, 1–15.
Mosteller, F., & Tukey, J. W. Data analysis, including statistics. In G. Lindzey & E. Aronson (Eds.),The handbook of social psychology (Vol. 2, 2nd ed.). Reading, Mass.: Addison-Wesley, 1968.
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)
Overall, J. E., & Woodward, J. A. A simple test for heterogeneity of variance in complex factorial designs.Psychometrika, 1974,39, 311–318.
Scheffé, H. A.The analysis of variance. New York: Wiley, 1959.
Zelen, M. Factorial experiments in life testing.Technometrics, 1959,1, 269–288.
Zelen, M. Analysis of two-factor classifications with respect to life tests. In I. Olkin, S. G. Ghurye, W. Hoeffding, W. G. Madow, & H. B. Mann (Eds.),Contributions to probability and statistics. Palo Alto: Stanford University Press, 1960.
Walsh, J. E. Concerning the effect of intraclass correlation on certain significant tests.Annals of Mathematical Statistics, 1947,18, 88–96.
Author information
Authors and Affiliations
Additional information
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.
Rights and permissions
About this article
Cite this article
O'Brien, R.G. Robust techniques for testing heterogeneity of variance effects in factorial designs. Psychometrika 43, 327–342 (1978). https://doi.org/10.1007/BF02293643
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02293643