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A Nonparametric Test Statistic for the General Linear Model

Author

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  • Michael R. Harwell
  • Ronald C. Serlin

Abstract

Puri and Sen (1969Puri and Sen (1985) presented a nonparametric test statistic based on a general linear model approach that is appropriate for testing a wide class of hypotheses. The two forms of this statistic, pure- and mixed-rank, differ according to whether the original predictor values or their ranks are used. Both forms permit the use of standard statistical packages to perform the analyses. The applicability of these statistics in testing a number of hypotheses is highlighted, and an example of their use is given. A simulation study for the multivariate-multiple-regression case is used to examine the distributional behavior of the pure- and mixed-rank statistics and an important competitor, the rank transformation of Conover and Iman (1981). The results suggest that the pure- and mixed-rank statistics are superior with respect to minimizing liberal Type I error rates, whereas the Conover and Iman statistic produces larger power values.

Suggested Citation

  • Michael R. Harwell & Ronald C. Serlin, 1989. "A Nonparametric Test Statistic for the General Linear Model," Journal of Educational and Behavioral Statistics, , vol. 14(4), pages 351-371, December.
    • Handle: RePEc:sae:jedbes:v:14:y:1989:i:4:p:351-371
    DOI: 10.3102/10769986014004351
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    Cited by:

    1. M Hashem Pesaran & Takashi Yamagata, 2024. "Testing for Alpha in Linear Factor Pricing Models with a Large Number of Securities," Journal of Financial Econometrics, Oxford University Press, vol. 22(2), pages 407-460.
    2. Gary van Vuuren & Riaan de Jongh, 2017. "A comparison of risk aggregation estimates using copulas and Fleishman distributions," Applied Economics, Taylor & Francis Journals, vol. 49(17), pages 1715-1731, April.

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