The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Simulation analysis of type I error and power for F test and rank transformed F test in $2 times 2$ factorial ANOVA

$2 times 2$ 요인 계획법의 F 검정과 순위 F 검정에 따른 제1종 오류와 검정력 분석에 대한 의태 연구

  • 최영훈 ((447-791) 경기도 오산시 양산동 411번지, 한신대학교 통계학과)
  • Published : 1995.09.01
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Abstract

When there is no main effcts or only one main effect in a $2 \times 2$ factorial design, Type I error rates and power for the rank transformed F test (FR test) for interaction are nearly equal to those of the classical F test. However the power of FR test is quite superior under the exponential distribution rather than the of FR test is quite superior under the exponential distribution rather than the normal distribution. Meanwhile when both main effects are in the model, Type I error rates of FR test, compared with those of F test, decrease as the effect size increases and are dependent on the fashion in which main effects are constructed. In addition, the power of FR test increases as the effect size and the sample size increase and is highly dependent on the manner in which main effects are constructed and the type of population distribution.

$2 \times 2$ 요인계획법에서 주효과가 전혀 존재하지 않거나 단지 하나만이 존재하는 경우의 교호작용을 위한 일반적인 F 검정과 순위변환을 이용한 F 검정 (FR 검정)의 제1종 오류율과 검정력은 전반적으로 비슷한 수준이나 정규분포보다는 지수분포하에서의 FR 검정의 검정력이 상당히 높은 수준임을 알 수 있다. 반면에 주효과들이 모두 존재하는 경우의 FR 검정의 제1종 오류율은 F 검정에 비하여 효과의 크기가 증가할수록 감소하고 주효과의 구성방법에도 영향을 받으며, 검정력은 효과의 크기와 표본의 크기를 크게할수록 증가하되 FR 검정의 검정력은 F 검정에 비하여 낮은 수준이며 주효과의 구성방법 및 모집단의 분포형태에 따라 민감하게 변화함을 알 수 있다.

Keywords

References

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