The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Nonparametric method using linear statistics in analysis of covariance model

공분산분석에서 선형위치통계량을 이용한 비모수 검정법

  • Choi, Yoonjung (Department of Biomedicine.Health Science, The Catholic University of Korea) ;
  • Kim, Dongjae (Department of Biomedicine.Health Science, The Catholic University of Korea)
  • 최윤정 (가톨릭대학교 의생명.건강과학과) ;
  • 김동재 (가톨릭대학교 의생명.건강과학과)
  • Received : 2017.03.08
  • Accepted : 2017.04.26
  • Published : 2017.06.30
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Abstract

Quade (1967) proposed RANK ANCOVA, which is a nonparametric method to test differences between treatments when there are covariates. Hwang and Kim (2012) also proposed a joint placement test on covariate-adjusted residuals. In this paper, we proposed a new nonparametric method to control the effect of covariate on a response variable that uses linear statistics on covariate adjusted-residuals. The score function used in the linear statistics was proposed by Jeon and Kim (2016). Monte Carlo simulation is also conducted to compare the empirical powers of the proposed method with previous methods.

공변량(covariate)이 존재하는 경우, 각 처리군 간 효과의 차이를 검정하기 위한 대표적인 비모수적 방법에는 Quade (1967)가 제안한 검정법이 있다. 또한 반응변수에 대해 공변량으로 단순선형회귀분석을 실시하여 얻은 잔차에 대해 일원배치분산분석과 Kruskal Wallis가 제안한 방법을 적용하는 방법, 그리고 Hwang과 Kim (2012)이 제안한 비모수적 도구인 위치(placement)를 이용한 방법이 있다. 본 논문에서는 공분산분석 모형에서 Hwang과 Kim (2012)이 제안한 방법을 확장하여 공분산분석에서의 새로운 방법을 제안하였다. 또한 모의실험(Monte Carlo simulation study)을 통하여 기존의 검정법들과 제안한 방법의 검정력을 비교하였다.

Keywords

References

  1. Ceyhan, E. and Goad, C. L. (2009). A comparison of analysis of covariate-adjusted Residuals and analysis of covariance, Communications in Statistics - Simulation and Computation, 38, 2019-2038. https://doi.org/10.1080/03610910903243687
  2. Chung, T. and Kim, D. (2007). Nonparametric method using placement in one-way layout, The Korean Communications in Statistics, 3, 552-560.
  3. Hwang, D. and Kim, d. (2012). Nonparametric Method Using Placement in Analysis of Covariance Model Communacations for Statistical Applications and Methods19, 721-729 https://doi.org/10.5351/CKSS.2012.19.5.721
  4. Hong, I. and Lee, S. (2014). Kruskal-Wallis one-way analysis of variance based on linear placements, Korean Mathematical Society, 51, 701-716. https://doi.org/10.4134/BKMS.2014.51.3.701
  5. Jeon, K. and Kim, D. (2016). Nonparametric method in one-way layout based on joint placement, The Korean Journal of Applied Statistics, 29, 729-739 https://doi.org/10.5351/KJAS.2016.29.4.729
  6. 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/10.1080/01621459.1952.10483441
  7. Lee, J. (2005). Statistical Method for Biotechnology Research, Freeacademy, Seoul.
  8. Quade, D. (1967). Rank analysis of covariance, Journal of the American Statistical Association, 62, 1187-1220. https://doi.org/10.1080/01621459.1967.10500925