Solutions to the Behrens-Fisher problem

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, identically and normal distributions. Few textbooks offer alternatives when one or more of the underlying assumptions are not defensible. We have developed an executable FORTRAN code for producing the statistics suggested by Cressie and Whitford, Yuen and Dixon, and Yuen. An executable FORTRAN is available from the author on request (e-mail only).