Some simple approximate solutions to the behrens-fisher problem
Osebekwin Ebenezer Asiribo, John Gurland · Communication in Statistics- Theory and Methods · 1989
Two approximate solutions to the problem of testing equality of means of two normal populations in the presence of variance heterogeneity are considered. The first is based on an estimate of the true critical function and the second on a statistic which appears in the leading term of some asymptotic solutions to the problem. These solutions are compared with other known tests such as Welch's approximate t and the Welch-Aspin test. The size of the first test is very close to that of Welch's t; and the second, although much simpler than the Welch-Aspin solution, controls the size as effectively and has virtually the same high power.