Contributions to two-sample statistics

Abstract

When testing the equality of the means from two independent normally distributed populations given that the variances of the two populations are unknown but assumed equal, the classical Student's two-sample t-test is recommended. If the underlying population distributions are normal with unequal and unknown variances, either Welch's t-statistic or Satterthwaite's approximate F test is suggested. However, Welch's procedure is non-robust under most non-normal distributions. There is a variable tolerance level around the strict assumptions of data independence, homogeneity of variances, and identical and normal distributions. Few textbooks offer alternatives when one or more of the underlying assumptions are not defensible. While there are more than a few non-parametric (rank) procedures that provide alternatives to Student's t-test, we restrict this review to the promising alternatives to Student's two-sample t-test in non-normal models.

Keywords:

• Robust two-sample t-tests
• symmetric trimmed means
• asymmetric trimmed means
• linear rank statistics
• transformation statistics