The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Nonparametric multiple comparison method using aligned method and joint placement in randomized block design with replications

반복이 있는 랜덤화 블록 모형에서 정렬방법과 결합위치를 이용한 비모수 다중비교법

  • Hwang, Juwon (Department of Biomedicine.Health Science, The Catholic University of Korea) ;
  • Kim, Dongjae (Department of Biomedicine.Health Science, The Catholic University of Korea)
  • 황주원 (가톨릭대학교 의생명.건강과학과) ;
  • 김동재 (가톨릭대학교 의생명.건강과학과)
  • Received : 2018.06.04
  • Accepted : 2018.08.30
  • Published : 2018.10.31
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Abstract

The method of Mack and Skillings (Technometrics, 23, 171-177, 1981) is a nonparametric multiple comparison method in a randomized block design with replications. This method is likely to result in loss of information because each block is ranked using the average of observations instead of repeated observations. In this paper, we proposed a new nonparametric multiple comparison method in the randomized block model with replications using an alignment method proposed by Hodges and Lehmann (The Annals of Mathematical Statistics, 33, 482-497, 1962) that extend the joint placement method proposed by Chung and Kim (Communications for Statistical Applications and Methods, 14, 551-560, 2007). In addition, Monte Carlo simulation compared the family wise error rate and power with the parametric method and the nonparametric method.

반복이 있는 랜덤화 블록 모형(randomized block design with replications)에서 비모수 다중비교 방법으로는 Mack과 Skillings (Technometrics, 23, 171-177, 1981) 방법이 있다. 이 방법은 각 블록의 처리에서 반복된 관측값 대신 관측값들의 평균을 이용해 순위를 매기기 때문에 정보의 손실이 발생할 가능성이 있다. 이를 보완하기 위해 본 논문에서는 Hodges와 Lehmann (The Annals of Mathematical Statistics, 33, 482-497, 1962)이 제안한 정렬방법과 Chung과 Kim (Communications for Statistical Applications and Methods, 14, 551-560, 2007)이 제안한 결합위치 검정법을 확장하여 반복이 있는 랜덤화 블록 모형에서 새로운 비모수 다중비교 방법을 제시하였다. 또한 몬테카를로 모의실험(Monte Carlo simulation)을 통해 모수적 방법과 기존의 비모수적 방법과의 family wise error rate (FWE)와 검정력을 비교하였다.

Keywords

References

  1. Chung, T. S. and Kim, D. J. (2007). Nonparametric method using placement in one-way layout, Communications for Statistical Applications and Methods, 14, 551-560. https://doi.org/10.5351/CKSS.2007.14.3.551
  2. Dun, O. J. (1964). Multiple comparisons using rank sums, Technometrics, 6, 241-252. https://doi.org/10.1080/00401706.1964.10490181
  3. Friedman, M. (1937). The use of ranks to avoid the assumption of normality implicit in the analysis of variance, Journal of the American Statistical Association, 32, 675-701. https://doi.org/10.1080/01621459.1937.10503522
  4. Han, J. U. and Kim, D. J. (2006). Nonparametric multiple comparison procedure using alignment method under randomized block design, The Korean Journal of Applied Statistics, 19, 555-564. https://doi.org/10.5351/KJAS.2006.19.3.555
  5. Hodges, J. L. and Lehmann, E. L. (1962). Rank methods for combination of independent experiments in analysis of variance, The Annals of Mathematical Statistics, 33, 482-497. https://doi.org/10.1214/aoms/1177704575
  6. Keuls, M. (1952). The use of the "studentized range" in connection with an analysis of variance, Euphytica, 1, 112-122. https://doi.org/10.1007/BF01908269
  7. Kramer, C. Y. (1956). Extension of multiple range tests to group means with unequal numbers of replications, Biometrics, 12, 307-310. https://doi.org/10.2307/3001469
  8. Kruskal, W. H. and Wallis, W. A. (1952). Use of ranks in one-criterion variance analysis, Journals of the American Statistical Association, 47, 583-621. https://doi.org/10.1080/01621459.1952.10483441
  9. Lee, E. and Kim, D. (2017). Nonparametric procedures using alignment method and joint placement in a randomized block design with replications, The Korean Journal of Applied Statistics, 30, 291-299. https://doi.org/10.5351/KJAS.2017.30.2.291
  10. Lee, M. H. and Kim, D. J. (2012). Nonparametric method using an alignment method in a randomized block design with replications, Communications for Statistical Applications and Methods, 19, 77-84. https://doi.org/10.5351/CKSS.2012.19.1.077
  11. Mack, G. A. and Skillings, J. H. (1981). On the use of a Friedman-type statistic in balanced and unbalanced block designs, Technometrics, 23, 171-177. https://doi.org/10.1080/00401706.1981.10486261
  12. Nemenyi, P. (1963). Distribution-free multiple comparisons (Ph. D. thesis), Princetion University.
  13. Orban, J. and Wolfe, D. A. (1982). A class of distribution-free two-sample tests based on placements, Journal of the American Statistical Association, 77, 666-671. https://doi.org/10.1080/01621459.1982.10477870
  14. Scheffe, H. (1953). A method for judging all contrasts in the analysis of variance, Biometrika, 40, 87-104.
  15. Song, H. and Kim, D. (2015). Understanding Statistics, Cheong Moon Gak, Seoul.
  16. Song, H. and Lee, H. (1995). Design of Clinical Experiments using SAS, Free Academy, Seoul.
  17. Song, M. and Jo, S. (2002). Analysis of Statistical Data using SAS, Free Academy, Seoul.
  18. Tukey, J. W. (1953). The Problem of Multiple Comparisons, Unpublished dotted notes, Princeton University, 396.