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.
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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).
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).
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).
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).
M. S. Bartlett, “Properties of sufficiency of statistical tests,” Proc. Roy. Soc., A 160, 268 (1937).
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).
H. O. Hartley, “The maximum F-ratio as a short-cut test of heterogeneity of variance,” Biometrika, 37, 308 (1950).
H. Levene, “Robust tests for equality of variances,” in: Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling (1960), p. 278.
A. R. Ansari and R. A. Bradley, “Rank-tests for dispersions,” Ann. Math. Stat., 31, 1174 (1960).
A. Mood, “On the asymptotic efficiency of certain nonparametric tests,” Ann. Math. Stat., 25, 514 (1954).
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).
J. Capon, “Asymptotic efficiency of certain locally most powerful rank tests,” Ann. Math. Stat., 32, 88 (1961).
J. Klotz, “Nonparametric tests for scale,” Ann. Math. Stat., 33, 498 (1962).
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).
B. Yu. Lemeshko, Statistical Analysis of Uniform Observations of Random Quantities: A Program System [in Russian], Izd. NGTU, Novosibirsk (1995).
L. N. Bolshev and N. V. Smirnov, Tables for Mathematical Statistics [in Russian], Nauka, Moscow (1983).
“Levene test for equality of variances,” in: Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/eda/section3/eda35a.htm (checked January 25, 2010).
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).
M. B. Brown and A. B. Forsythe, “Robust tests for equality of variances,” J. Amer. Stat. Assoc., 69, 364 (1974).
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Translated from Izmeritel’naya Tekhnika, No. 3, pp. 10–16, March, 2010.
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Lemeshko, B.Y., Lemeshko, S.B. & Gorbunova, A.A. Application and power of criteria for testing the homogeneity of variances. Part I. Parametric criteria. Meas Tech 53, 237–246 (2010). https://doi.org/10.1007/s11018-010-9489-7
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DOI: https://doi.org/10.1007/s11018-010-9489-7