Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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Asymptotic Relative Efficiency of t-test Following Transformations

  • Yeo, In-Kwon (Department of Statistics, University of Wisconsin, Madison, WI 53706, USA)
  • Published : 1997.12.01
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Abstract

The two-sample t-test is not expected to be optimal when the two samples are not drawn from normal populations. According to Box and Cox (1964), the transformation is estimated to enhance the normality of the tranformed data. We investigate the asymptotic relative efficiency of the ordinary t-test versus t-test applied transformation introduced by Yeo and Johnson (1997) under Pitman local alternatives. The theoretical and simulation studies show that two-sample t-test using transformed date gives higher power than ordinary t-test for location-shift models.

Keywords

References

  1. Plots, Transformations and Regression Atkinson, A. C.
  2. Annals of Statistics v.23 Tests Following Transformations Chen, H.
  3. Annals of Statistics v.20 Bounds on AREs of Tests Following Box-Cox Transformations Chen, H.;Loh, W. Y.
  4. Journal of the Royal Statistical Society, series B v.26 An Analysis of Transformations Box, G. E. P.;Cox, D. R.
  5. Journal of the American Statistical Association v.78 Statistical Tests Based on Transformed Data Doksum, K. A.;Wong, C. W.
  6. Annals of Mathematical Statistics v.27 Uniform Convergence of Random Functions with Applications to Statistics Rubin, H.
  7. Convex Transformations of Random Variables VAN ZWET, W. R.
  8. A New Family of Power Transformations to Improve Normality or Symmetry. (summit to Annals of Statistics, ms 857) Yeo, I. K.;Johnson, R. A.