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A Levene-type test of homogeneity of variances against ordered alternatives

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  • Philip Pallmann
  • Ludwig Hothorn
  • Gemechis Djira

Abstract

Investigations focusing on differences in scale parameters across multiple samples appear in various scientific fields, e.g., when assessing measurement precision. In such cases a natural order of groups often suggests itself, which can be exploited by tests involving ordered alternatives. We propose multiple contrast tests with order-restriction based on robust Levene residuals as a powerful approach to detect scale differences between several groups. The proposed method is applied to a real data set and also extensive simulation is conducted to assess power and robustness against non-normality. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Philip Pallmann & Ludwig Hothorn & Gemechis Djira, 2014. "A Levene-type test of homogeneity of variances against ordered alternatives," Computational Statistics, Springer, vol. 29(6), pages 1593-1608, December.
    • Handle: RePEc:spr:compst:v:29:y:2014:i:6:p:1593-1608
    DOI: 10.1007/s00180-014-0508-z
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    References listed on IDEAS

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    1. Bretz, Frank, 2006. "An extension of the Williams trend test to general unbalanced linear models," Computational Statistics & Data Analysis, Elsevier, vol. 50(7), pages 1735-1748, April.
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    4. Singh, Parminder & Gill, Amar Nath & Kumar, Narendra, 2009. "A test of homogeneity of several variances against tree ordered alternative," Statistics & Probability Letters, Elsevier, vol. 79(22), pages 2315-2320, November.
    5. Peng, J. & Lee, C.I.C. & Liu, L. & Jiang, J., 2006. "Orthogonal multiple contrast test for testing monotone on the average," Statistics & Probability Letters, Elsevier, vol. 76(2), pages 161-168, January.
    6. Konietschke Frank & Bösiger Sandra & Brunner Edgar & Hothorn Ludwig A., 2013. "Are Multiple Contrast Tests Superior to the ANOVA?," The International Journal of Biostatistics, De Gruyter, vol. 9(1), pages 63-73, August.
    7. Kimihiro Noguchi & Yulia Gel, 2010. "Combination of Levene-type tests and a finite-intersection method for testing equality of variances against ordered alternatives," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(7), pages 897-913.
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    9. Cahoy, Dexter O., 2010. "A bootstrap test for equality of variances," Computational Statistics & Data Analysis, Elsevier, vol. 54(10), pages 2306-2316, October.
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    Cited by:

    1. Philip Pallmann & Ludwig A. Hothorn, 2016. "Analysis of means: a generalized approach using R," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(8), pages 1541-1560, June.

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