Journal of the Korean Data and Information Science Society

한국데이터정보과학회 (The Korean Data and Information Science Society)
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4 × 4 그레코라틴방격모형의 검정력 연구

Power study for 4 × 4 graeco-latin square design

  • 최영훈 (한신대학교 응용통계학과)
  • 투고 : 2012.05.29
  • 심사 : 2012.06.22
  • 발행 : 2012.07.31
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초록

$4{\times}4$ 그레코라틴방격모형은 모집단의 분포에 상관없이 주효과 검정을 위한 순위변환 통계량의 검정력이 모수적 통계량의 검정력보다 전체적으로 높은 우위성을 갖는다. 효과크기가 균등간격이 아닌 경우에 주효과 검정을 위한 순위변환 통계량의 검정력은 효과크기가 균등간격인 경우보다 다소 낮지만 모수적 통계량의 검정력에 비하여 월등한 비교우위를 갖는다. 순위변환 통계량의 검정력은 블럭효과의 수가 줄어들거나 효과크기가 작아질수록 모수적 통계량의 검정력보다 월등히 우세함을 보인다. 블럭효과들이 존재할 때는 주효과에 비하여 블럭효과들이 모두 작거나 하나의 블럭효과에 편중된 경우에 순위변화 통계량의 검정력이 모수적 통계량의 검정력보다 더욱 우수하다. 이는 상호작용없이 다인자인 네 개의 주인자 및 블럭인자만으로 구성된 그레코라틴방격모형의 특성에 의한 결과로, 앞으로 구체화하지 못한 다인자로 구성된 요인실험계획모형 등에 확대 적용할 순위변환기법의 가능성을 제시한다.

In $4{\times}4$ graeco-latin square design, powers of rank transformed statistic for testing the main effect are superior to powers of parametric statistic without regard to the effect structure with equally or unequally spaced effect levels as well as the type of population distributions such as exponential, double exponential, normal and uniform distribution. As numbers of block effect or effect sizes are decreased, powers of rank transformed statistic are much higher than powers of parametric statistic. In case that block effects are smaller than a main effect or one block effect is higher than other block effects, powers of rank transformed statistic are much higher than powers of parametric statistic in $4{\times}4$ graeco-latin square design with three block effects and one main effect.

키워드

참고문헌

  1. Akritas, M. G. and Papadatos, N. (2004). Heteroscedastic one way ANOVA and lack of fit tests. Journal of the American Statistical Association, 99, 368-382. https://doi.org/10.1198/016214504000000412
  2. Choi, Y. H. (2009). Power analysis for 3 x 3 latin square design. Journal of the Korean Data & Information Science Society, 20, 401-410.
  3. Choi, Y. H. (2011). Power analysis for 2 x 2 factorial in randomized complete block design. Journal of the Korean Data & Information Science Society, 22, 245-253.
  4. Conover, W. J. and Iman, R. L. (1981). Rank transformations as a bridge between parametric and nonparametric statistics. The American Statistician, 35, 124-128.
  5. Fabian, V. (1991). On the problem of interactions in the analysis of variance. Journal of the American Statistical Association, 86, 362-374. https://doi.org/10.1080/01621459.1991.10475048
  6. Fisher, R. A. and Yates, F. (1953). Statistical tables for biological, agricultural, and medical research, 4th edition, Oliver and Boyd, Edinburgh.
  7. Hicks, C. R. (1982). Fundamental concepts in the design of experiments, 3rd edition, Holt, Rinehart and Winston, New York.
  8. Hora, S. C. and Iman, R. L. (1988). Asymptotic relative efficiencies of the rank transformation procedure in randomized complete block design. Journal of the American Statistical Association, 83, 462-470. https://doi.org/10.1080/01621459.1988.10478618
  9. Lee, C., Kang, H. and Sim, S. (2012). An implementation of the sample size and the power for testing mean and proportion. Journal of the Korean Data & Information Science Society, 23, 53-61. https://doi.org/10.7465/jkdi.2012.23.1.053
  10. Lee, S. and Kim D. (2011). Nonparametric procedures using placement in randomized block design with replications. Journal of the Korean Data & Information Science Society, 22, 1105-1112.
  11. Montgomery, D. C. (1991). Design and analysis of experiments, 3rd edition, John Wiley & Sons, New York.
  12. Neter, J., Wasserman, W. and Kutner, M. (1990). Applied linear statistical models, 3rd edition, Irwin, Homewood and Boston.
  13. Thompson, G, L. (1991). A note on the rank transform for interactions. Biometrika, 78, 697-701. https://doi.org/10.1093/biomet/78.3.697

피인용 문헌

  1. Power and major gene-gene identification of dummy multifactor dimensionality reduction algorithm vol.24, pp.2, 2013, https://doi.org/10.7465/jkdi.2013.24.2.277
  2. Power study for 2 × 2 factorial design in 4 × 4 latin square design vol.25, pp.6, 2014, https://doi.org/10.7465/jkdi.2014.25.6.1195
  3. Derivation of error sum of squares of two stage nested designs and its application vol.24, pp.6, 2013, https://doi.org/10.7465/jkdi.2013.24.6.1439