Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Nonparametric Method Using Placement in One-way Layout

  • Chung, Taek-Su (Department of Biostatistics, The Catholic University of Korea) ;
  • Kim, Dong-Jae (Department of Biostatistics, The Catholic University of Korea)
  • Published : 2007.12.31
Download PDF
⟨ Previous Next ⟩

Abstract

Kruskal and Wallis (1952) proposed typical nonparametric method in one-way layout problem. A special feature of this procedure is use of rank in mixed samples. In this paper, the new procedure based on placement as extension of the two sample placement tests described in Orban and Wolfe (1982) was proposed. Some critical values in small sample cases and comparative results of a Monte Carlo power study are presented.

Keywords

References

  1. Bhapkar, V. P. (1961). A nonparametric test for the problem of sevral samples. The Annals of Mathematical Statistics, 32, 1108-1117 https://doi.org/10.1214/aoms/1177704849
  2. Chacko, V. J. (1963). Testing homogeneity against ordered alternatives. The Annals of Mathematical Statistics, 34, 945-956 https://doi.org/10.1214/aoms/1177704017
  3. Jonckheere, A. R. (1954). A distribution-free k-sample test against ordered alternatives. Biometrika, 41, 133-145 https://doi.org/10.1093/biomet/41.1-2.133
  4. Kruskal, W. H. and Wallis, W. A (1952). Use of ranks in one-criterion variance analysis. Journal of the American Statistical Association, 47, 583-621 https://doi.org/10.2307/2280779
  5. Mann, H. B. and Whitney, D. R.(1947). On a test of whether one of the two random variables is stochastically larger than the other. The Annals of Mathematical Statistics, 18, 50-60 https://doi.org/10.1214/aoms/1177730491
  6. Orban, J. and Wolfe, D. A. (1982). A class of distribution-free two-sample tests based on placement. Journal of the American Statistical Association, 77, 666-672 https://doi.org/10.2307/2287734
  7. Puri, M. L. (1965). On the combination of independent two sample tests of a general class. Review of the International Statistical Institute, 33, 229-241 https://doi.org/10.2307/1402029
  8. Schulzer, M. (1969). Contributions to the k-sample problem: A symmetric statistic. The Annals of Mathematical statistics, 40, 1933-1949 https://doi.org/10.1214/aoms/1177697277
  9. Terpstra, T. J. (1952). The asymptotic normality and consistency of kendall's test against trend, when ties are present in one ranking. Indagationes Mathematicae, 14, 327-333
  10. SAS Release 8.1 (1998). Cary SAS Institute

Cited by

  1. Nonparametric procedures using aligned method and joint placement in randomized block design vol.24, pp.1, 2013, https://doi.org/10.7465/jkdi.2013.24.1.95
  2. The asymptotic behavior of linear placement statistics vol.81, pp.2, 2011, https://doi.org/10.1016/j.spl.2010.10.021
  3. Nonparametric Method using Placement in an Analysis of a Covariance Model vol.19, pp.5, 2012, https://doi.org/10.5351/CKSS.2012.19.5.721
  4. Nonparametric Method in One-way Layout for Umbrella Alternatives based on Placement vol.28, pp.6, 2015, https://doi.org/10.5351/KJAS.2015.28.6.1181