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A New Powerful Nonparametric Rank Test for Ordered Alternative Problem

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  • Guogen Shan
  • Daniel Young
  • Le Kang

Abstract

We propose a new nonparametric test for ordered alternative problem based on the rank difference between two observations from different groups. These groups are assumed to be independent from each other. The exact mean and variance of the test statistic under the null distribution are derived, and its asymptotic distribution is proven to be normal. Furthermore, an extensive power comparison between the new test and other commonly used tests shows that the new test is generally more powerful than others under various conditions, including the same type of distribution, and mixed distributions. A real example from an anti-hypertensive drug trial is provided to illustrate the application of the tests. The new test is therefore recommended for use in practice due to easy calculation and substantial power gain.

Suggested Citation

  • Guogen Shan & Daniel Young & Le Kang, 2014. "A New Powerful Nonparametric Rank Test for Ordered Alternative Problem," PLOS ONE, Public Library of Science, vol. 9(11), pages 1-10, November.
    • Handle: RePEc:plo:pone00:0112924
    DOI: 10.1371/journal.pone.0112924
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    References listed on IDEAS

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    1. M. A. Fligner & D. A. Wolfe, 1982. "Distribution‐free tests for comparing several treatments with a control," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 36(3), pages 119-127, September.
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    Cited by:

    1. Jeremias Leão & Francisco Cysneiros & Helton Saulo & N. Balakrishnan, 2016. "Constrained test in linear models with multivariate power exponential distribution," Computational Statistics, Springer, vol. 31(4), pages 1569-1592, December.
    2. Charles A. Holt & Sean P. Sullivan, 2023. "Permutation tests for experimental data," Experimental Economics, Springer;Economic Science Association, vol. 26(4), pages 775-812, September.

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