New Nonparametric Rank-Based Tests for Paired Data

DOI: 10.4236/ojs.2014.47047   PDF   HTML     3,582 Downloads   4,443 Views   Citations


We propose a new nonparametric test based on the rank difference between the paired sample for testing the equality of the marginal distributions from a bivariate distribution. We also consider a modification of the novel nonparametric test based on the test proposed by Baumgartern, Weiβ, and Schindler (1998). An extensive numerical power comparison for various parametric and nonparametric tests was conducted under a wide range of bivariate distributions for small sample sizes. The two new nonparametric tests have comparable power to the paired t test for the data simulated from bivariate normal distributions, and are generally more powerful than the paired t test and other commonly used nonparametric tests in several important bivariate distributions.

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Shan, G. (2014) New Nonparametric Rank-Based Tests for Paired Data. Open Journal of Statistics, 4, 495-503. doi: 10.4236/ojs.2014.47047.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Shapiro, S.S. and Wilk, M.B. (1965) An Analysis of Variance Test for Normality (Complete Samples). Biometrika, 52, 591-611.
[2] Shan, G.G., Vexler, A., Wilding, G. and Hutson, A. (2011) Simple and Exact Empirical Likelihood Ratio Tests for Normality Based on Moment Relations. Communications in Statistics: Simulation and Computation, 40, 129-146.
[3] Wilcoxon, F. (1945) Individual Comparisons by Ranking Methods. Biometrics Bulletin, 1, 80-83.
[4] Mann, H.B. and Whitney, D.R. (1947) On a Test of Whether One of Two Random Variables Is Stochastically Larger than the Other. Annals of Mathematical Statistics, 18, 50-60.
[5] Lam, F.C. and Longnecker, M.T. (1983) A Modified Wilcoxon Rank Sum Test for Paired Data. Biometrika, 70, 510-513.
[6] Shan, G.G., Ma, C.X., Hutson, A.D. and Wilding, G.E. (2013) Some Tests for Detecting Trends Based on the Modified Baumgartner Weiβ Schindler Statistics. Computational Statistics & Data Analysis, 57, 246-261.
[7] Fay, M.P. and Proschan, M.A. (2010) Wilcoxon-Mann-Whitney or t-Test? On Assumptions for Hypothesis Tests and Multiple Interpretations of Decision Rules. Statistics Surveys, 4, 1-39.
[8] Baumgartner, W., Weiβ, P. and Schindler, H. (1998) A Nonparametric Test for the General Two-Sample Problem. Biometrics, 54, 1129-1135.
[9] Neuhäuser, M. (2001) One-Sided Two-Sample and Trend Tests Based on a Modified Baumgartner-Weiβ Schindler Statistic. Journal of Nonparametric Statistics, 13, 729-739.
[10] Murakami, H. (2006) A k-Sample Rank Test Based on Modified Baumgartner Statistic and Its Power Comparison. Journal of the Japanese Society of Computational Statistics, 19, 1-13.
[11] Kundu, D. and Gupta, R.D. (2009) Bivariate Generalized Exponential Distribution. Journal of Multivariate Analysis, 100, 581-593.
[12] Antonisamy, B., Christopher, S. and Samuelson, P. (2010) Biostatistics: Principles and Practice. McGraw-Hill Education, New York.
[13] Wilding, G.E., Shan, G. and Hutson, A.D. (2012) Exact Two-Stage Designs for Phase II Activity Trials with Rank-Based Endpoints. Contemporary Clinical Trials, 33, 332-341.
[14] Shan, G., Ma, C., Hutson, A.D. and Wilding, G.E. (2012) An Efficient and Exact Approach for Detecting Trends with Binary Endpoints. Statistics in Medicine, 31, 155-164.
[15] Shan, G. and Ma, C. (2012) Unconditional Tests for Comparing Two Ordered Multinomials. Statistical Methods in Medical Research, Published Online.
[16] Shan, G. (2013) More Efficient Unconditional Tests for Exchangeable Binary Data with Equal Cluster Sizes. Statistics & Probability Letters, 83, 644-649.
[17] Shan, G. (2013) A Note on Exact Conditional and Unconditional Tests for Hardy-Weinberg Equilibrium. Human Heredity, 76, 10-17.
[18] Shan, G. and Ma, C. (2014) Exact Methods for Testing the Equality of Proportions for Binary Clustered Data from Otolaryngologic Studies. Statistics in Biopharmaceutical Research, 6, 115-122.
[19] Shan, G., Ma, C., Hutson, A.D. and Wilding, G.E. (2013) Randomized Two-Stage Phase II Clinical Trial Designs Based on Barnard’s Exact Test. Journal of Biopharmaceutical Statistics, 23, 1081-1090.
[20] Shan, G. (2014) Exact Approaches for Testing Non-Inferiority or Superiority of Two Incidence Rates. Statistics & Probability Letters, 85, 129-134.
[21] Jonckheere, A.R. (1954) A Distribution-Free k-Sample Test against Ordered Alternatives. Biometrika, 41, 133-145.
[22] Terpstra, T.J. (1952) The Asymptotic Normality and Consistency of Kendall’s Test against Trend, When Ties Are Present in One Ranking. Indigationes Mathematicae, 14, 327-333.
[23] Shan, G., Hutson, A.D. and Wilding, G.E. (2012) Two-Stage k-Sample Designs for the Ordered Alternative Problem. Pharmaceutical Statistics 11, 287-294.
[24] Page, E.B. (1963) Ordered Hypotheses for Multiple Treatments: A Significance Test for Linear Ranks. Journal of the American Statistical Association, 58, 216-230.

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