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Nonparametric multiple contrast tests for general multivariate factorial designs

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  • Gunawardana, Asanka
  • Konietschke, Frank

Abstract

We develop purely nonparametric multiple inference methods for general multivariate data that neither assume any specific data distribution nor identical covariance matrices across the treatment groups. Continuous, discrete, and even ordered categorical (ordinal) data can be analyzed with these procedures in a unified way. To test hypotheses formulated in terms of purely nonparametric treatment effects, we derive pseudo-rank based multiple contrast tests and simultaneous confidence intervals. Hereby, the simultaneous confidence intervals are compatible with the multiple comparisons. The small-sample performance of the procedures is examined in a simulation study which indicates that the proposed procedures (i) control the family-wise error rate quite accurately and (ii) have a substantially higher power under non-normality than mean-based parametric competing methods. Application of the proposed tests is demonstrated by analyzing a real data set.

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  • Gunawardana, Asanka & Konietschke, Frank, 2019. "Nonparametric multiple contrast tests for general multivariate factorial designs," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 165-180.
    • Handle: RePEc:eee:jmvana:v:173:y:2019:i:c:p:165-180
    DOI: 10.1016/j.jmva.2019.02.016
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    References listed on IDEAS

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    1. Bathke, Arne C. & Harrar, Solomon W. & Madden, Laurence V., 2008. "How to compare small multivariate samples using nonparametric tests," Computational Statistics & Data Analysis, Elsevier, vol. 52(11), pages 4951-4965, July.
    2. 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.
    3. Genest, Christian & Nešlehová, Johanna, 2007. "A Primer on Copulas for Count Data," ASTIN Bulletin, Cambridge University Press, vol. 37(2), pages 475-515, November.
    4. Edgar Brunner & Frank Konietschke & Markus Pauly & Madan L. Puri, 2017. "Rank-based procedures in factorial designs: hypotheses about non-parametric treatment effects," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1463-1485, November.
    5. Munzel, Ullrich, 1999. "Linear rank score statistics when ties are present," Statistics & Probability Letters, Elsevier, vol. 41(4), pages 389-395, February.
    6. Harrar, Solomon W. & Bathke, Arne C., 2008. "Nonparametric methods for unbalanced multivariate data and many factor levels," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1635-1664, September.
    7. Edgar Brunner & Madan Puri, 2001. "Nonparametric methods in factorial designs," Statistical Papers, Springer, vol. 42(1), pages 1-52, January.
    8. Burchett, Woodrow W. & Ellis, Amanda R. & Harrar, Solomon W. & Bathke, Arne C., 2017. "Nonparametric Inference for Multivariate Data: The R Package npmv," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 76(i04).
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    Cited by:

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    3. Nowak, Claus P. & Konietschke, Frank, 2021. "Simultaneous inference for Kendall’s tau," Journal of Multivariate Analysis, Elsevier, vol. 185(C).

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