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.
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References
Alvo, M., and P. Cabilio. 1995. Testing ordered alternatives in the presence of incomplete data. J. Am. Stat. Assoc., 90, 1015–1024.
Daniel, W. W. 1990. Applied nonparametric statistics, 2nd ed. Boston, MA: PWS-Kent Publishing Company.
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.
Durbin, J. 1951. Incomplete blocks in ranking experiments. Br. J. Psychol. Stat. Section, V.4, 85–90.
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.
Friedman, M. 1940. A comparison of alternative tests of significance for the problem of m Rankings. Ann. Math. Stat., 11, 86–92.
Jonckheere, A. R. 1954. A distribution-free k-sample test against ordered alternatives. Biometrika, 41, 133–145.
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.
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.
Mack, G. A., and D. A. Wolfe. 1981. K-sample rank tests for umbrella alternatives. J. Am. Stat. Assoc., 76, 175–181.
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.
Magel, R., J. Terpstra, K. Canonizado, and J. I. Park. 2010. Nonparametric tests for mixed designs. Commun. Stat. Simulation Comput., 39(6), 1228–1250.
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.
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.
Page, E. B. 1963. Ordered hypotheses for multiple treatments: A significance test for linear ranks. J. Am. Stat. Assoc., 58, 216–230.
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.
Wilcoxon, F. 1945. Individual comparisons by ranking methods. Biometrics, 1, 80–83.
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Magel, R.C., Fu, R. Proposed Nonparametric Test for the Mixed Two-Sample Design. J Stat Theory Pract 8, 221–237 (2014). https://doi.org/10.1080/15598608.2014.847768
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DOI: https://doi.org/10.1080/15598608.2014.847768