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Measurement Techniques
Published in: Measurement Techniques 5/2017

18-08-2017

Application and Power of Parametric Criteria for Testing the Homogeneity of Variances. Part IV

Authors: B. Yu. Lemeshko, T. S. Sataeva

Published in: Measurement Techniques | Issue 5/2017

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Abstract

The application of parametric criteria for testing the homogeneity of variances (Bartlett, Cochran, Fisher, Hartley, Levene, Neyman–Pearson, O’Brien, Link, Newman, Bliss–Cochran–Tukey, Cadwell–Leslie–Brown, the Overall–Woodward Z-test and modified Z-test) is examined, including under conditions such that the standard assumption of normality is violated. A comparative analysis is made of the power of the criteria. The permissible level of significance is estimated for the case in which the distributions of the statistics for the applied tests are unknown.
previous article Development of the Concept of Uncertainty in Measurement and Revision of the Guide to the Expression of Uncertainty in Measurement. Part 2. Comparative Analysis of Basic Provisions of the Guide and Their Planned Changes
next article Modeling, Reproduction, and Mapping of Geofields with and Without Measurement Noise. Part 4. Spline, Geostatistical, and Fuzzy Regression Analysis Techniques

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Literature
1.
B. Yu. Lemeshko and T. S. Sataeva, “Application and power of parametric criteria for testing the homogeneity of variances, Part 3,” Izmer. Tekhn., No. 1, 8–13 (2017).
2.
B. Yu. Lemeshko, S. B. Lemeshko, and A. A. Gorbunova, “Application and power of criteria for testing the homogeneity of variances. Part I. Parametric criteria,” Izmer. Tekhn., No. 3, 10–16 (2010).
3.
B. Yu. Lemeshko, S. B. Lemeshko, and A. A. Gorbunova, “Application and power of criteria for testing the homogeneity of variances. Part 2. Nonparametric criteria,” Izmer. Tekhn., No. 5, 11–18 (2010).
4.
A. I. Kobzar’, Applied Mathematical Statistics for Engineers and Scientific Workers, FIZMATLIT, Moscow (2006).
5.
R. G. O’Brien, “Robust techniques for testing heterogeneity of variance effects in factorial designs,” Psychometrika, 43, No. 3, 327–342 (1978).
6.
R. F. Link, “The sampling distribution of the ratio of two ranges from independent samples,” Ann. Math. Stat., 21, No. 1, 112–116 (1950).MathSciNetCrossRefMATH
7.
D. Newman, “The distribution of range in samples from a normal population, expressed in terms of an independent estimate of standard deviation,” Biometrika, 31, 20–30 (1939).MathSciNetCrossRefMATH
8.
C. I. Bliss, W. G. Cochran, and J. W. Tukey, “A rejection criterion based upon the range,” Biometrika, 43, 418–422 (1956).CrossRefMATH
9.
R. T. Leslie and B. M. Brown, “Use of range in testing heterogeneity of variance,” Biometrika, 53, 221–227 (1966).MathSciNetCrossRef
10.
J. E. Overall and J. A. Woodward, “A simple test for heterogeneity of variance in complex factorial design,” Psychometrica, 39, 311–318 (1974).CrossRefMATH
11.
J. E. Overall and J. A. Woodward, A Robust and Powerful Test for Heterogeneity of Variance, Univ. of Texas Med. Branch Psychometric Lab. (1976).
12.
M. S. Bartlett, “Properties of sufficiency of statistical tests,” Proc. Roy. Soc. A., 160, 268–287 (1937).ADSCrossRefMATH
13.
W. G. Cochran, “The distribution of the largest of a set of estimated variances as a fraction of their total,” Ann. Eugenics, 11, 47–52 (1941).MathSciNetCrossRefMATH
14.
L. N. Bol’shev and N. V. Smirnov, Tables of Mathematical Statistics, Nauka, Moscow (1983).MATH
15.
H. O. Hartley, “The maximum F-ratio as a short-cut test of heterogeneity of variance,” Biometrika, 37, 308–312 (1950).MathSciNetMATH
16.
H. Levene, “Robust tests for equality of variances,” Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling (1960), pp. 278–292.
17.
18.
19.
S. Siegel and J. W. Tukey, “A nonparametric sum of rank procedure for relative spread in unpaired samples,” J. Amer. Stat. Ass., 55, No. 291, 429–445 (1960).MathSciNetCrossRefMATH
20.
21.
M. A. Fligner and T. J. Killeen, “Distribution-free two-sample tests for scale,” J. Amer. Stat. Ass., 71, No. 353, 210–213 (1976).MathSciNetCrossRefMATH
22.
B. Yu. Lemeshko, Criteria for Testing the Deviation of a Distribution from Normal. Guidance for Applications, INFRA-M, Moscow (2015), DOI 10.1273/6086.
23.
A. A. Gorbunova and B. Yu. Lemeshko, “Application of variance homogeneity tests under violation of normality assumption,” in: Proc. lnt. Workshop Applied Methods of Statistical Analysis. Simulations and Statistical Inference, AMSA’2011, Novosibirsk, Russia, Sept. 20–22, 2011, pp. 28–36.
24.
B. Yu. Lemeshko, S. B. Lemeshko, and A. P. Rogozhnikov, “Real-time studying of statistic distributions of non-parametric goodness-of-fit tests when testing complex hypotheses,” ibid., pp. 19–27.
25.
B. Yu. Lemeshko, A. A. Gorbunova, S. B. Lemeshko, and A. P. Rogozhnikov, “Application of nonparametric goodness-of-fit tests for composite hypotheses in case of unknown distributions of statistics,” in: Proc. Int. Workshop Applied Methods of Statistical Analysis. Applications in Survival Analysis, Reliability and Quality Control, AMSA’2013, Novosibirsk, Russia, Sept. 25–27, 2013, pp. 8–24.
26.
B. Yu. Lemeshko and S. N. Postovalov, Computer Technologies for Data Analysis and Studies of Statistical Behavior: Textbook, NGTU, Novosibirsk (2004).MATH
27.
28.
B. Yu. Lemeshko, “On the identification of a distribution law for the random component of measurement error,” Metrologiya, No. 7, 8–17 (2004).
Metadata
Title
Application and Power of Parametric Criteria for Testing the Homogeneity of Variances. Part IV
Authors
B. Yu. Lemeshko
T. S. Sataeva
Publication date
18-08-2017
Publisher
Springer US
Published in
Measurement Techniques / Issue 5/2017
Print ISSN: 0543-1972
Electronic ISSN: 1573-8906
DOI
https://doi.org/10.1007/s11018-017-1213-4

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