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

Computational Statistics volume 29, pages 1593–1608 (2014)Cite this article

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.

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Authors and Affiliations

  1. Institute of Biostatistics, Leibniz University Hannover, Herrenhaeuser Strasse 2, 30419 , Hannover, Germany

    Philip Pallmann & Ludwig A. Hothorn

  2. Department of Mathematics and Statistics, South Dakota State University, Brookings, SD , 57007, USA

    Gemechis D. Djira

Authors
  1. Philip Pallmann
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  2. Ludwig A. Hothorn
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  3. Gemechis D. Djira
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Corresponding author

Correspondence to Philip Pallmann.

Additional information

The work of the second author (LAH) was partly supported by the German Science Foundation grant DFG-HO1687. The authors wish to thank the editor and two anonymous referees for hints and suggestions that helped improve the manuscript.

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Pallmann, P., Hothorn, L.A. & Djira, G.D. A Levene-type test of homogeneity of variances against ordered alternatives. Comput Stat 29, 1593–1608 (2014). https://doi.org/10.1007/s00180-014-0508-z

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  • DOI: https://doi.org/10.1007/s00180-014-0508-z

Keywords

  • Levene residuals
  • Heterogeneous variances
  • Trend test
  • Multiple contrasts
  • Order-restricted inference