Skip to main content
SpringerLink
Log in

A simple test for heterogeneity of variance in complex factorial designs

  • Published:
Psychometrika Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Bartlett, M. S. Properties of sufficiency and statistical tests.Proceedings of the Royal Society of London, Series A, 1937,160, 268–282.

    Google 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, 128–138.

    Google Scholar 

  • Box, G. E. P. A general distribution theory for a class of likelihood criteria.Biometrika, 1949,36, 317–346.

    Google Scholar 

  • Box, G. E. P. Non-normality and tests on variance.Biometrika, 1953,40, 318–335.

    Google Scholar 

  • Fisher, R. A. and Yates, F.Statistical Tables for Biological Agricultural and Medical Research. New York: Hafner, 1963.

    Google Scholar 

  • Marascuilo, L. A. Large-sample multiple comparisons.Psychological Bulletin, 1966,65, 280–290.

    Google Scholar 

  • Overall, J. E. and Henry, B. W. Decisions about drug therapy: III: Selection of treatment for psychiatric inpatients.Archives of General Psychiatry, 1973,28, 81–89.

    Google Scholar 

  • Scheffé, H.The Analysis of Variance. New York: Wiley, 1959.

    Google 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).

Download references

Author information

Authors and Affiliations

  1. The University of Texas Medical Branch, Galveston

    John E. Overall & J. Arthur Woodward

Authors
  1. John E. Overall
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Arthur Woodward
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

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

Rights and permissions

Reprints and permissions

About this article

Cite this article

Overall, J.E., Arthur Woodward, J. A simple test for heterogeneity of variance in complex factorial designs. Psychometrika 39, 311–318 (1974). https://doi.org/10.1007/BF02291705

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02291705

Keywords

Search

Navigation