Advertisement

Journal of Statistical Theory and Practice

, Volume 8, Issue 2, pp 221–237 | Cite as

Proposed Nonparametric Test for the Mixed Two-Sample Design

  • Rhonda C. Magel
  • Ran Fu
Article

Abstract

A nonparametric test is proposed for a mixed design consisting of a paired sample portion and a two-independent-sample portion to test for a difference in treatment effects. The test is compared on the basis of estimated powers to a test developed by Dubnicka, Blair, and Hettmansperger (2002). Situations are found in which the proposed test has higher powers and situations are found in which the Dubnicka et al. test has higher powers.

Keywords

Paired data Independent two-sample data Mann-Whitney test Wilcoxon signed-rank test 

AMS Subject Classification

62G 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alvo, M., and P. Cabilio. 1995. Testing ordered alternatives in the presence of incomplete data. J. Am. Stat. Assoc., 90, 1015–1024.MathSciNetCrossRefGoogle Scholar
  2. Daniel, W. W. 1990. Applied nonparametric statistics, 2nd ed. Boston, MA: PWS-Kent Publishing Company.Google Scholar
  3. Dubnicka, S. R., R. C. Blair, and T. P. Hettmansperger. 2002. Rank-based procedures for mixed pairs and two-sample designs. J. Modern Appl. Stat. Methods, 1(1). 32–41.CrossRefGoogle Scholar
  4. Durbin, J. 1951. Incomplete blocks in ranking experiments. Br. J. Psychol. Stat. Section, V.4, 85–90.CrossRefGoogle Scholar
  5. Friedman, M. 1937. The use of ranks to avoid the assumption of normality implicit in the analysis of variance. J. Am. Stat. Assoc., 32, 675–701.CrossRefGoogle Scholar
  6. Friedman, M. 1940. A comparison of alternative tests of significance for the problem of m Rankings. Ann. Math. Stat., 11, 86–92.MathSciNetCrossRefGoogle Scholar
  7. Jonckheere, A. R. 1954. A distribution-free k-sample test against ordered alternatives. Biometrika, 41, 133–145.MathSciNetCrossRefGoogle Scholar
  8. Kruskal, W. H., and W. A. Wallis. 1953. Use of ranks in one-criterion variance analysis. J. Am. Stat. Assoc., 58, 583–621. Addendum, 48, 907–911.MATHGoogle Scholar
  9. Kim, D. H., and Y. C. Kim. 1992. Distribution-free tests for umbrella alternatives in a randomized block design. J. Nonparametric Stat., 1, 277–285.MathSciNetCrossRefGoogle Scholar
  10. Mack, G. A., and D. A. Wolfe. 1981. K-sample rank tests for umbrella alternatives. J. Am. Stat. Assoc., 76, 175–181.MathSciNetGoogle Scholar
  11. Magel, R., J. Terpstra, and J. Wen. 2009. Proposed tests for the nondecreasing alternative in a mixed design. J. Stat. Manage. Systems, 12, 963–977.MathSciNetCrossRefGoogle Scholar
  12. Magel, R., J. Terpstra, K. Canonizado, and J. I. Park. 2010. Nonparametric tests for mixed designs. Commun. Stat. Simulation Comput., 39(6), 1228–1250.MathSciNetCrossRefGoogle Scholar
  13. Magel, R., L. Cao, and A. Ndungu. 2012. Comparing the Durbin, Wilcoxon signed ranks test, and a proposed test in balanced incomplete block designs. Int. J. Sci. Society, 3, 1–16.CrossRefGoogle Scholar
  14. Mann, H. B., and D. R. Whitney. 1947. On a test of whether one of two random variables is stochastically larger than the other. Ann. Math. Stat., 18, 50–60.MathSciNetCrossRefGoogle Scholar
  15. Page, E. B. 1963. Ordered hypotheses for multiple treatments: A significance test for linear ranks. J. Am. Stat. Assoc., 58, 216–230.MathSciNetCrossRefGoogle Scholar
  16. Terpstra, T. J. 1952. The asymptotic normality and consistency of Kendall’s test against trend, when ties are present in one ranking. Indagationes Math., 14, 327–333.MathSciNetCrossRefGoogle Scholar
  17. Wilcoxon, F. 1945. Individual comparisons by ranking methods. Biometrics, 1, 80–83.MathSciNetCrossRefGoogle Scholar

Copyright information

© Grace Scientific Publishing 2014

Authors and Affiliations

  1. 1.Department of StatisticsNorth Dakota State UniversityFargoUSA

Personalised recommendations