The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Nonparametric method in randomized block design for umbrella alternatives based on aligned method and placement

랜덤화 블록 계획법에서 우산형 대립가설에 대한 정렬방법과 위치를 이용한 비모수 검정법

  • Kim, Jeonghyun (Department of Biomedicine.Health Science, The Catholic University of Korea) ;
  • Kim, Dongjae (Department of Biomedicine.Health Science, The Catholic University of Korea)
  • 김정현 (가톨릭대학교 의생명.건강과학과) ;
  • 김동재 (가톨릭대학교 의생명.건강과학과)
  • Received : 2016.09.30
  • Accepted : 2016.11.18
  • Published : 2016.12.31
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Abstract

Nonparametric methods in randomized block design were suggested by Friedman (1937) for general alternatives and were also proposed by Page (1963) for ordered alternatives in one-way layout; in addition, K-sample rank tests for umbrella alternatives were suggested by Mack and Wolfe (1981). In this paper, we proposed a nonparametric method of umbrella alternatives for randomized block design using the aligned method proposed by Hodges and Lehmann (1962) to use block information and using placement suggested by Kim (1999). Monte Carlo simulation was also adapted to compare the power of the proposed procedure with previous methods.

랜덤화 블록 계획법(randomized block design)에서 대립가설형태에 따라 많은 비모수적인 방법들이 제안되었다. 일반대립가설에서 대표적으로 Fridman (1937)의 검정법이 있고, 순서형 대립가설에서는 Page (1963)의 검정법이 있다. 우산형 대립가설에 대한 비모수적 방법으로는 일원 배치 모형에서 k개의 표본 문제에 대하여 Mack과 Wolfe (1981)의 검정법이 있다. 본 논문에서는 랜덤화 블록 계획법(randomized block design)에서 우산형대립가설에 대하여 블록 간의 정보를 이용한 Hodges와 Lehmann (1962)의 정렬방법과 위치를 이용한 Kim (1999)의 검정법을 이용하여 검정법을 제안하였다. 또한, Monte carlo 모의실험을 통하여 제안된 검정법과 기존의 검정법을 비교하였다.

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References

  1. Alvo, M. (2008). Nonparametric tests of hypotheses for umbrella alternatives, Canadian Journal of Statistics, 36, 143-156. https://doi.org/10.1002/cjs.5550360113
  2. Bhat, S. V. (2009). Simple k-sample rank tests for umbrella alternatives, Research Journal of Mathematics and Statistics, 1, 27-29.
  3. Chen, Y. I. and Wolfe, D. A. (1990). A study of distribution-free tests for umbrella alternatives, Biometrical Journal, 32, 47-57. https://doi.org/10.1002/bimj.4710320109
  4. Chen, Y. I. and Wolfe, D. A. (1993). Nonparametric procedures for comparing umbrella pattern treatment effects with a control in a one-way layout, Biometrics, 49, 455-465. https://doi.org/10.2307/2532558
  5. 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
  6. Hettmansperger, T. P. and Norton, R. M. (1987). Tests for patterned alternatives in k-sample problems, Journal of the American Statistical Association, 82, 292-299.
  7. 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
  8. Kim, D. (1999). A class of distribution-free treatments versus control tests based on placements, Far East Journal of Theoretical Statistics, 3, 19-33.
  9. Kim, H. and Kim, D. (2016). Nonparametric procedures based on aligned method and placement for ordered alternatives in randomized block design, Journal of the Korean Data and Information Science Society, 29, 707-717.
  10. Kim, D., Lee, S., and Wang, W. (2011). The asymptotic behavior of linear placement statistics, Statistics and Probability Letters, 81, 326-336. https://doi.org/10.1016/j.spl.2010.10.021
  11. Lee, S. and Kim, D. (2011). Nonparametric procedures using placement in randomized block design with replications, Journal of the Korean Data and Information Science Society, 22, 1105-1112.
  12. Mack, G. A. and Wolfe, D. A. (1981). K-sample rank tests for umbrella alternatives, Journal of the American Statistical Association, 76, 175-181.
  13. Mann, H. B. and Whitney, D. R. (1947). On a test of whether one of two random variables is stochastically larger than the other, The Annals of Mathematical Statistics, 18, 50-60. https://doi.org/10.1214/aoms/1177730491
  14. 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, 666-671. https://doi.org/10.1080/01621459.1982.10477870
  15. Page, E. B. (1963). Ordered hypotheses for multiple treatments: a significance test for linear ranks, Journals of the American Statistical Association, 58, 216-230. https://doi.org/10.1080/01621459.1963.10500843
  16. Salman A. S. (2010). A new nonparametric test for the umbrella alternative (Master's Thesis), University of North Dakota, North Dakota.
  17. Song, H. and Kim, D. (1997). Statistics, Cheongmoongak, Seoul.