Improved statistics for contrasting means of two samples under non-normality.
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.
Xu
Jin
J
Department of Statistics, East China Normal University, Shanghai, China.
Cui
Xinping
X
Gupta
Arjun K
AK
D002648:Child; D002675:Child, Preschool; D003627:Data Interpretation, Statistical; D004410:Dyslexia / Q000175:diagnosis / Q000523:psychology; D005260:Female; D006801:Humans; D008137:Longitudinal Studies; D008297:Male; D015233:Models, Statistical; D009483:Neuropsychological Tests / Q000706:statistics & numerical data; D016011:Normal Distribution; D011594:Psychometrics / Q000706:statistics & numerical data*