응용통계연구 (The Korean Journal of Applied Statistics)

  • 제30권5호
  • /
  • Pages.691-699
  • /
  • 2017
  • /
  • 1225-066X(pISSN)
  • /
  • 2383-5818(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지
DOI QR코드

DOI QR Code

정규 모집단의 평균 비교를 위한 신뢰구간 겹치기 시각화

Visual inspection of overlapping confidence intervals for comparison of normal population means

  • 투고 : 2017.07.17
  • 심사 : 2017.09.23
  • 발행 : 2017.10.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

두 개의 정규 모집단의 평균이 같은가를 검증할 때 두 개의 신뢰구간이 겹치는 지를 시각적으로 판단하여 결정하는 방법은 매우 직관적이면서도 사용하기 쉽다. 그러나 신뢰구간이 겹칠 때도 두 집단의 평균은 통계적으로 유의하게 다를 수 있으므로 가설검증 결과와 다를 수 있다. 평균 차에 대한 신뢰구간을 각 평균의 신뢰구간으로 변환한 후에 두 신뢰구간이 겹치는지 여부를 시각적으로 판단하여 가설검증을 할 수 있는 방법을 제안한다. 또한 이 방법은 분산이 같은 k개의 정규 모집단의 평균을 비교할 경우에도 사용할 수 있음을 보인다.

Data analysts sometimes test the equality of two normal population means by the inspection of the overlapping of two confidence intervals. This method seems simple to use; however, it is a common statistical misconception to suppose that two normal means are not significantly different because of no overlapping. This article will present transforming the confidence interval of the mean difference to individual confidence intervals that are visualized to inspect overlapping. It will also be shown that this technique can be extended when comparing the k normal population means with equal variances.

키워드

참고문헌

  1. Browne, R. H. (1979). On visual assessment of the significance of a mean difference, Biometrics, 35, 657-665. https://doi.org/10.2307/2530259
  2. Cumming, G. (2009). Inference by eye: reading the overlap of independent confidence intervals, Statistics in Medicine, 28, 205-220. https://doi.org/10.1002/sim.3471
  3. Cumming, G. and Calin-Jageman, R. J. (2017). Introduction to the New Statistics: Estimation, Open Science, and Beyond, Routledge, New York.
  4. Gardner, M. J. and Altman, D. G. (1986). Confidence intervals rather than P values: estimation rather than hypothesis testing, British Medical Journal, 292, 746-750. https://doi.org/10.1136/bmj.292.6522.746
  5. Goldstein, H. and Healy, M. J. R. (1995). The graphical presentation of a collection of means, Journal of the Royal Statistical Society A, 158, 175-177. https://doi.org/10.2307/2983411
  6. Maghsoodloo, S. and Huang, C. (2010). Comparing the overlapping of two independent confidence intervals with a single confidence interval for two normal population parameters, Journal of Statistical Planning and Inference, 140, 3295-3305. https://doi.org/10.1016/j.jspi.2010.04.057
  7. Payton, M. E., Greenstone, M. H., and Schenker, N. (2003). Overlapping confidence intervals or standard error intervals:what do they mean in terms of statistical significance?, The Journal of Insect Science, 3, 34-39.
  8. Schenker, N. and Gentleman, J. F. (2001). On judging the significance of differences by examining the overlap between confidence intervals, The American Statistician, 55, 182-186. https://doi.org/10.1198/000313001317097960
  9. Tryon, W. W. (2001). Evaluating statistical difference, equivalence, and indeterminacy using inferential confidence intervals: an integrated alternative method of conducting null hypothesis statistical tests, Psychological Methods, 6, 371-386. https://doi.org/10.1037/1082-989X.6.4.371