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Correlation coefficients between nonparametric tests for location and scale

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Summary

In attempting to find the most practical and efficient nonparametric rank test in the two-sample problem of testing for equality of populations, it is submitted that correlation coefficients might be useful. As a measure of the strength of the linear relationship between comparable test statistics, the correlation helps to determine how the tests distinguish between rank orders in the null distribution. This paper gives expressions for the correlations between Gastwirth's percentile-modifiedT p±Br tests, the Wilcoxon test, Barton-David test, Mood test and Savage tests, and indicates how they could be used in choosing which test to employ in practice, including optimal selection ofp andr in the percentile-modified tests.

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References

  1. A. R. Ansari and R. A. Bradley, “Rank-sum tests for dispersions,”Ann. Math. Statist., 31 (1960), 1174–1189.

    Article  MATH  MathSciNet  Google Scholar 

  2. D. E. Barton and F. N. David, “A test for birth-order effects,”Annals of Eugenics, 22 (1958), 250–257.

    MATH  Google Scholar 

  3. H. Chernoff and I. R. Savage, “Asymptotic normality and efficiency of certain nonparametric test statistics,”Ann. Math. Statist., 29 (1958), 972–994.

    Article  MathSciNet  Google Scholar 

  4. J. E. Freund and A. R. Ansari, “Two-way rank sum tests for variances,”Virginia Polytechnic Institute Report, 1957.

  5. C. van Eeden, “The relation between Pitman's asymptotic relative efficiency of two tests and the correlation coefficient between their test statistics,”Ann. Math. Statist., 34 (1963), 1442–1451.

    Article  MATH  MathSciNet  Google Scholar 

  6. J. L. Gastwirth, “Percentile modifications of two sample rank tests,”J. Amer. Statist. Ass., 60 (1965), 1127–1141.

    Article  MATH  MathSciNet  Google Scholar 

  7. J. D. Gibbons, “A proposed two-sample rank test: The Psi test and its properties,”J. R. Statist. Soc., B, 26 (1964), 305–312.

    MATH  MathSciNet  Google Scholar 

  8. J. H. Klotz, “Nonparametric tests for scale,”Ann. Math. Statist., 33 (1962), 498–512.

    Article  MATH  MathSciNet  Google Scholar 

  9. H. B. Mann and D. R. Whitney, “On a test whether one of two random variables is stochastically larger than the other,”Ann. Math. Statist., 18 (1947), 50–60.

    Article  MATH  MathSciNet  Google Scholar 

  10. A. M. Mood, “On the asymptotic efficiency of certain nonparametric two-sample tests,”Ann. Math. Statist., 25 (1954), 514–522.

    Article  MATH  MathSciNet  Google Scholar 

  11. I. R. Savage, “Contributions to the theory of rank order statistics—the two-sample case,”Ann. Math. Statist., 27 (1956), 590–615.

    Article  MATH  MathSciNet  Google Scholar 

  12. Siegel, Sidney and J. W. Tukey, “A non-parametric sum of ranks procedure for relative spread in unpaired samples,”J. Amer. Statist. Ass., 55 (1960), 429–445.

    Article  MathSciNet  Google Scholar 

  13. M. E. Terry, “Some rank-order tests which are most powerful against specific parametric alternatives,”Ann. Math. Statist., 23 (1952), 346–366.

    Article  MATH  MathSciNet  Google Scholar 

  14. F. Wilcoxon, “Individual comparisons by ranking methods,”Biometrics, 1 (1945), 80–83.

    Article  Google Scholar 

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Authors and Affiliations

  1. University of Pennsylvania, Pennsylvania, USA

    Jean D. Gibbons

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  1. Jean D. Gibbons
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Gibbons, J.D. Correlation coefficients between nonparametric tests for location and scale. Ann Inst Stat Math 19, 519–526 (1967). https://doi.org/10.1007/BF02911701

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  • DOI: https://doi.org/10.1007/BF02911701

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