Hostname: page-component-745bb68f8f-lrblm Total loading time: 0 Render date: 2025-01-07T17:25:39.173Z Has data issue: false hasContentIssue false
  • English
  • Français

A Simple Test for Heterogeneity of Variance in Complex Factorial Designs

Published online by Cambridge University Press:  01 January 2025

John E. Overall  and
J. Arthur Woodward
John E. Overall
Affiliation:
The University of Texas Medical Branch, Galveston
J. Arthur Woodward
Affiliation:
The University of Texas Medical Branch, Galveston
Get access Rights & Permissions [Opens in a new window]

Abstract

A simple procedure for testing heterogeneity of variance is developed which generalizes readily to complex, multi-factor experimental designs. Monte Carlo Studies indicate that the Z-variance test statistic presented here yields results equivalent to other familiar tests for heterogeneity of variance in simple one-way designs where comparisons are feasible. The primary advantage of the Z-variance test is in the analysis of factorial effects on sample variances in more complex designs. An example involving a three-way factorial design is presented.

Type
Original Paper
Information
Psychometrika , Volume 39 , Issue 3 , September 1974 , pp. 311 - 318
Copyright
Copyright © 1974 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

*

This work was supported in part by grant DHEW 2 RO 1 MH 14675-06 from the Psychopharmacology Research Branch, NIMH.

References

Bartlett, M. S. Properties of sufficiency and statistical tests. Proceedings of the Royal Society of London, Series A, 1937, 160, 268–282Google Scholar
Bartlett, M. S. and Kendall, D. G. The statistical analysis of variance—heterogeneity and the logarithmic transformation. Journal of the Royal Statistical Society, Series B, 1946, 8, 128–138CrossRefGoogle Scholar
Box, G. E. P. A general distribution theory for a class of likelihood criteria. Biometrika, 1949, 36, 317–346CrossRefGoogle ScholarPubMed
Box, G. E. P. Non-normality and tests on variance. Biometrika, 1953, 40, 318–335CrossRefGoogle Scholar
Fisher, R. A. and Yates, F. Statistical Tables for Biological Agricultural and Medical Research, 1963, New York: HafnerGoogle Scholar
Marascuilo, L. A. Large-sample multiple comparisons. Psychological Bulletin, 1966, 65, 280–290CrossRefGoogle ScholarPubMed
Overall, J. E. and Henry, B. W. Decisions about drug therapy: III: Selection of treatment for psychiatric inpatients. Archives of General Psychiatry, 1973, 28, 81–89CrossRefGoogle Scholar
Scheffé, H. The Analysis of Variance, 1959, New York: WileyGoogle Scholar
Woodward, J. A. and Overall, J. E. Computer generation of random normal deviates for Monte Carlo work. Perceptual and Motor Skills, 1975 (in press).Google Scholar