응용통계연구 (The Korean Journal of Applied Statistics)

  • 제22권6호
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  • Pages.1249-1263
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  • 2009
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  • 1225-066X(pISSN)
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  • 2383-5818(eISSN)
한국통계학회 (The Korean Statistical Society)
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단변량 및 이변량 순위변수의 비모수적 윌콕슨 검정법에 의한 표본수 결정방법

Sample Size Determination of Univariate and Bivariate Ordinal Outcomes by Nonparametric Wilcoxon Tests

  • 박해강 (가톨릭대학교 의과대학 의학통계학과) ;
  • 송혜향 (가톨릭대학교 의과대학 의학통계학과)
  • Park, Hae-Gang (Department of Biostatistics, Medical College, The Catholic University of Korea) ;
  • Song, Hae-Hiang (Department of Biostatistics, Medical College, The Catholic University of Korea)
  • 투고 : 20090800
  • 심사 : 20091000
  • 발행 : 2009.12.31
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초록

표본수 결정에서 요구되는 검정력 함수는 연구가설에 상응하는 가장 적절한 검정방법에 의한 것이어야 한다. 의학연구의 논문에 자주 나타나는 순위자료 또는 범주형 빈도자료의 분석에는 비모수적 방법이 적절하며, 본 논문에서는 단변량 및 이변량 순위변수에 대한 윌콕슨-만-휘트니(Wilcoxon-Mann-Whitney; WMW) 검정법에 의한 표본수 결정방법을 제시한다. 단변량 순위변수의 윌콕슨 검정에서는 귀무가설과 대립가설 하의 분산을 이용한 표본수 공식이 귀무가설 하의 분산만 이용한 표본수 공식보다 정확하지만, 대립가설 하의 분산식에 나타나는 확률값이 일반적으로 알려져 있지 않으므로 이 확률값의 추정이 문제가 된다. 모의실험으로 두 방법에 대한 장, 단점을 알아본다. 효능과 안전성의 이변량 순위변수에서는 이변량 WMW 검정법에 의한 표본수 결정방법이 모수적 검정법에 의한 표본수 결정방법보다 더욱 바람직하다.

The power function in sample size determination has to be characterized by an appropriate statistical test for the hypothesis of interest. Nonparametric tests are suitable in the analysis of ordinal data or frequency data with ordered categories which appear frequently in the biomedical research literature. In this paper, we study sample size calculation methods for the Wilcoxon-Mann-Whitney test for one- and two-dimensional ordinal outcomes. While the sample size formula for the univariate outcome which is based on the variances of the test statistic under both null and alternative hypothesis perform well, this formula requires additional information on probability estimates that appear in the variance of the test statistic under alternative hypothesis, and the values of these probabilities are generally unknown. We study the advantages and disadvantages of different sample size formulas with simulations. Sample sizes are calculated for the two-dimensional ordinal outcomes of efficacy and safety, for which bivariate Wilcoxon-Mann-Whitney test is appropriate than the multivariate parametric test.

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참고문헌

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