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Nonparametric test for the homogeneity of the overall variability

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  • Ashis SenGupta
  • Hon Keung Tony Ng

Abstract

In this paper, we propose a nonparametric test for homogeneity of overall variabilities for two multi-dimensional populations. Comparisons between the proposed nonparametric procedure and the asymptotic parametric procedure and a permutation test based on standardized generalized variances are made when the underlying populations are multivariate normal. We also study the performance of these test procedures when the underlying populations are non-normal. We observe that the nonparametric procedure and the permutation test based on standardized generalized variances are not as powerful as the asymptotic parametric test under normality. However, they are reliable and powerful tests for comparing overall variability under other multivariate distributions such as the multivariate Cauchy, the multivariate Pareto and the multivariate exponential distributions, even with small sample sizes. A Monte Carlo simulation study is used to evaluate the performance of the proposed procedures. An example from an educational study is used to illustrate the proposed nonparametric test.

Suggested Citation

  • Ashis SenGupta & Hon Keung Tony Ng, 2011. "Nonparametric test for the homogeneity of the overall variability," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(9), pages 1751-1768, September.
    • Handle: RePEc:taf:japsta:v:38:y:2011:i:9:p:1751-1768
    DOI: 10.1080/02664763.2010.529876
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    References listed on IDEAS

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    1. J. Carlos Garcia-Diaz, 2007. "The 'effective variance' control chart for monitoring the dispersion process with missing data," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 1(1), pages 40-55.
    2. Bhandary, Madhusudan, 1996. "Test for generalized variance in signal processing," Statistics & Probability Letters, Elsevier, vol. 27(2), pages 155-162, April.
    3. SenGupta, Ashis, 1987. "Tests for standardized generalized variances of multivariate normal populations of possibly different dimensions," Journal of Multivariate Analysis, Elsevier, vol. 23(2), pages 209-219, December.
    4. Isabel Parra-Frutos, 2009. "The behaviour of the modified Levene’s test when data are not normally distributed," Computational Statistics, Springer, vol. 24(4), pages 671-693, December.
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    1. Dariush Najarzadeh, 2019. "Testing equality of standardized generalized variances of k multivariate normal populations with arbitrary dimensions," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(4), pages 593-623, December.

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