DOI QR코드

DOI QR Code

Note on the Equality of Variances in Two Sample t-Test

두 집단 평균 차이 검정에서 분산의 동질성에 관한 소고

  • Kim, Sang-Cheol (Department of Applied Statistics, Yonsei University) ;
  • Lim, Jo-Han (Department of Statistics, Seoul National University)
  • Published : 2010.01.31

Abstract

Introductory statistic class proposes two tests for the equality of two population means according to the homogeneity of their variances. However, in practice, the variances are also unknown and practitioners often test their homogeneity before they do two sample t-test. This is also true in many popular statistical packages such as SAS and SPSS. In this paper, we study the type I error of this two stage procedure and propose a procedure to control it at a given significance level.

References

  1. Gurland, J. and McCullouch, R. S. (1962). Testing equality of means after a preliminary test of equality of variances, Biometrika, 49, 403-416. https://doi.org/10.1093/biomet/49.3-4.403
  2. Moser, B. K. and Stevens, G. R. (1992). Homogeneity of variance in the two-sample means test, The American Statistician, 46, 19-21. https://doi.org/10.2307/2684403
  3. Moser, B. K., Stevens, G. R. and Watts, C. L. (1989). The two-sample T test versus satterthwaite's approximate F test, Communication in Statistics - Theory and Method, 18, 3963-3975. https://doi.org/10.1080/03610928908830135