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Br J Math Stat Psychol. 2009 Feb;62(Pt 1):21-40. Epub 2007 Sep 29.

Improved statistics for contrasting means of two samples under non-normality.

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Department of Statistics, East China Normal University, Shanghai, China.


This paper presents the asymptotic expansions of the distributions of the two-sample t-statistic and the Welch statistic, for testing the equality of the means of two independent populations under non-normality. Unlike other approaches, we obtain the null distributions in terms of the distribution and density functions of the standard normal variable up to n(-1), where n is the pooled sample size. Based on these expansions, monotone transformations are employed to remove the higher-order cumulant effect. We show that the new statistics can improve the precision of statistical inference to the level of o (n(-1)). Numerical studies are carried out to demonstrate the performance of the improved statistics. Some general rules for practitioners are also recommended.

[Indexed for MEDLINE]

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