Measurement Techniques

, Volume 53, Issue 3, pp 237–246 | Cite as

Application and power of criteria for testing the homogeneity of variances. Part I. Parametric criteria

  • B. Yu. Lemeshko
  • S. B. Lemeshko
  • A. A. Gorbunova
General Problems of Metrology and Measurements Technique

A comparative analysis is made of the power of classical (Fisher, Bartlett, Cochran, Hartley, and Levene) tests of variance homogeneity. The distributions of the statistics of the tests are studied when the assumption that the sample obeys a normal law breaks down.

Key words

tests of homogeneity of variances Fisher Bartlett Cochran Hartley and Levene tests power of tests 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    B. Yu. Lemeshko and S. B. Lemeshko, “Statistical distribution convergence and homogeneity test power for Smirnov and Lehmann–Rosenblatt tests,” Izmer. Tekhn., No. 12, 9 (2005); Measur. Techn., 48, No. 12, 1159 (2005).Google Scholar
  2. 2.
    B. Yu. Lemeshko and S. B. Lemeshko, “Power and robustness of criteria used to verify the homogeneity of means,” Izmer. Tekhn., No. 9, 23 (2008); Measur. Techn., 51, No. 9, 950 (2008).Google Scholar
  3. 3.
    B. Yu. Lemeshko and E. P. Mirkin, “Bartlett and Cochran tests in measurements with probability laws different from normal,” Izmer. Tekhn., No. 10, 10 (2004); Measur. Techn., 47, No. 10, 960 (2004).Google Scholar
  4. 4.
    B. Yu. Lemeshko and V. M. Ponomarenko, “Distributions of the statistics used for testing hypotheses of equal variances for non-normal law error,” Nauch. Vestnik NGTU, No. 2 (23), 21 (2006).Google Scholar
  5. 5.
    M. S. Bartlett, “Properties of sufficiency of statistical tests,” Proc. Roy. Soc., A 160, 268 (1937).CrossRefADSGoogle Scholar
  6. 6.
    W. G. Cochran, “The distribution of the largest of a set of estimated variances as a fraction of their total,” Ann. Eugenics, 11, 47 (1941).MathSciNetGoogle Scholar
  7. 7.
    H. O. Hartley, “The maximum F-ratio as a short-cut test of heterogeneity of variance,” Biometrika, 37, 308 (1950).MATHMathSciNetGoogle Scholar
  8. 8.
    H. Levene, “Robust tests for equality of variances,” in: Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling (1960), p. 278.Google Scholar
  9. 9.
    A. R. Ansari and R. A. Bradley, “Rank-tests for dispersions,” Ann. Math. Stat., 31, 1174 (1960).MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    A. Mood, “On the asymptotic efficiency of certain nonparametric tests,” Ann. Math. Stat., 25, 514 (1954).MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    S. Siegel and J. W. Tukey, “A nonparametric sum of rank procedure for relative spread in unpaired samples,” J. Acoustic. Soc. America, 55, 429 (1960).MathSciNetGoogle Scholar
  12. 12.
    J. Capon, “Asymptotic efficiency of certain locally most powerful rank tests,” Ann. Math. Stat., 32, 88 (1961).MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    J. Klotz, “Nonparametric tests for scale,” Ann. Math. Stat., 33, 498 (1962).MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    B. Yu. Lemeshko and S. N. Postovalov, Computer Technology for Data Analysis and Investigation of Statistical Behavior: A Textbook [in Russian], Izd. NGTU, Novosibirsk (2004).Google Scholar
  15. 15.
    B. Yu. Lemeshko, Statistical Analysis of Uniform Observations of Random Quantities: A Program System [in Russian], Izd. NGTU, Novosibirsk (1995).Google Scholar
  16. 16.
    L. N. Bolshev and N. V. Smirnov, Tables for Mathematical Statistics [in Russian], Nauka, Moscow (1983).Google Scholar
  17. 17.
    “Levene test for equality of variances,” in: Handbook of Statistical Methods, (checked January 25, 2010).
  18. 18.
    J. H. Neel and W. M. Stallings, “A Monte Carlo study of Levene’s test of homogeneity of variance: empirical frequencies of type I error in normal distributions,” Paper Presented at the Annual Meeting of the American Educational Research Association Convention, Chicago, Illinois (April 1974).Google Scholar
  19. 19.
    M. B. Brown and A. B. Forsythe, “Robust tests for equality of variances,” J. Amer. Stat. Assoc., 69, 364 (1974).MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  • B. Yu. Lemeshko
    • 1
  • S. B. Lemeshko
    • 1
  • A. A. Gorbunova
    • 1
  1. 1.Novosibirsk State Technical UniversityNovosibirskRussia

Personalised recommendations