Robust techniques for testing heterogeneity of variance effects in factorial designs

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 ofs2 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.

[1]  H. Scheffé The Analysis of Variance , 1960 .

[2]  Rupert G. Miller The jackknife-a review , 1974 .

[3]  John E. Overall,et al.  A simple test for heterogeneity of variance in complex factorial designs , 1974 .

[4]  Paul A. Games,et al.  Robust Tests for Homogeneity of Variance , 1972 .

[5]  H. L. Gray,et al.  The Generalised Jackknife Statistic , 1974 .

[6]  J. Walsh Concerning the Effect of Intraclass Correlation on Certain Significance Tests , 1947 .

[7]  George Marsaglia,et al.  One-line random number generators and their use in combinations , 1968, Commun. ACM.

[8]  Mark I. Appelbaum,et al.  Some problems in the nonorthogonal analysis of variance. , 1974 .

[9]  Morton B. Brown,et al.  Robust Tests for the Equality of Variances , 1974 .

[10]  Marvin Zelen,et al.  Factorial Experiments in Life Testing , 1959 .

[11]  Patrick L. Odell,et al.  The effects of intraclass correlation on certain significance tests when sampling from multivariate normal population , 1974 .

[12]  P. Gartside,et al.  A Study of Methods for Comparing Several Variances , 1972 .

[13]  M. Layard,et al.  Robust Large-Sample Tests for Homogeneity of Variances , 1973 .

[14]  H. Levene Robust tests for equality of variances , 1961 .

[15]  Maurice G. Kendall,et al.  The advanced theory of statistics , 1945 .

[16]  K. J. Levy An empirical comparison of theZ-variance and Box-Scheffé tests for homogeneity of variance , 1975 .

[17]  W. Hays Statistics for the social sciences , 1973 .

[18]  G. Glass,et al.  Consequences of Failure to Meet Assumptions Underlying the Fixed Effects Analyses of Variance and Covariance , 1972 .

[19]  M. Kendall,et al.  The advanced theory of statistics , 1945 .

[20]  Charles G. Martin Comment on Levy's “an empirical comparison of the Z-variance and Box-Scheffé tests for homogeneity of variance” , 1976 .

[21]  W. Strawderman The Generalized Jackknife Statistic , 1973 .

[22]  S. L. Andersen,et al.  Permutation Theory in the Derivation of Robust Criteria and the Study of Departures from Assumption , 1955 .