Robustness of Two-Sample Tests for Variances

  • Gerd Nürnberg
Part of the Theory and Decision Library book series (TDLB, volume 1)


12 two sample-test for variances are investigated for robustness against violations of the assumed normal distribution by means of simulation. The degree of non-normality is discribed by the parameters skewness (γ1) and kurtosis (γ2). The real risk of first kind α and the power function (at 3 points) of the 12 tests are determined for the sample sizes n = 6, 18, 42 and different pairs of (γ1, γ2)-values.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bartlett, M.S. Properties of sufficiency and statistical tests. Proc. Roy. Soc. A 160 (1937) 268–282.CrossRefGoogle Scholar
  2. Bartlett, M. S., Kendall, D. G. The statistical analysis of variance heterogeneity and the logarithmic transformation. J. R. S. S. 8 (1946) 128–138.MathSciNetGoogle Scholar
  3. Box, G. E. P. Non-normality and tests on variance. Biometrika 40 (1953) 318–335.MathSciNetzbMATHGoogle Scholar
  4. Box, G. E. P., Andersen, S. L. Permutation theory in the derivation of robust criteria and the study of departures from assumptions. J. R. S. S., Ser. B 17 (1955) 1–34.zbMATHGoogle Scholar
  5. Brown, M. B., Forsythe, A. B. Robust tests for the equality of variances. JASA 69 (1974) 362 p. 364–367.zbMATHGoogle Scholar
  6. Fleishman, A. I. A method for simulating non-normal distributions. Psychometrika 43 (1978) 521–532.zbMATHCrossRefGoogle Scholar
  7. Games, P. A., Winkler, H. B.. Probert, D. A. Robust tests for homogeneity of variance. Educational and Psychological Measurement 32 (1972) 887–909.Google Scholar
  8. Geng, S., Wang, W. J., Miller, C. Small sample size comparisons of tests for homogeneity of variances by Monte-Carlo. Comm. Statist-Simulation Comp. B 8 (1979) 4, 379–389.CrossRefGoogle Scholar
  9. Herrendörfer, G. (ed.) Robustheit I. (1980) Probleme der angewandten Statistik Heft 4, AdL der DDR, Forschungszentrum für Tierproduktion Dum-merstorf-Rostock.Google Scholar
  10. Layard, M. W. J. Robust large-sample tests for homogeneity of variances. JASA 68 (1973) 195–198.Google Scholar
  11. Levene, H. Robust Tests for Equality of Variances. Contributions to probability and statistics, Stanford, University Press (1960) 278–292.Google Scholar
  12. Miller, R. G. jr. Jackknifing Variances. AMS 39 (1968) 567–582.zbMATHGoogle Scholar
  13. Ode, R. E., Evans, J. O. The percentage points of the normal distribution. Algorithm AS 70, Appl. Stat. 23 (1974) 96–97.Google Scholar
  14. Overall, J. F., Woodward, J. A.: A simple test for heterogeneity of variance in complex factorial designs. Psychometrika 39 (1974) 311–318.zbMATHCrossRefGoogle Scholar
  15. Scheffe, H.: Dispersiony analiz. Gousudarstwennoe Izdatel’stvo Fiziko-Matematiceskoj Literatury, Moskva, 1963.Google Scholar

Copyright information

© Academy of Agricultural Sciences of the GDR, Research Centre of Animal Production, Dummerstorf-Rostock, DDR 2551 Dummerstorf. 1984

Authors and Affiliations

  • Gerd Nürnberg
    • 1
  1. 1.Academy of Agricultural Sciences of the GDRResearch Centre of Animal Production Dummerstorf-RostockGermany

Personalised recommendations