Power Comparisons of Solutions to the Behrens-Fisher Problem

SYNOPTIC ABSTRACT

The problem that arises, when testing the equality of means from two independent normal populations without the assumption of equality of variances, is known as Behrens – Fisher problem. In the literature several approximate solutions to the Behrens – Fisher problem have been proposed and evaluated with respect to type I and type II error rates. Saxena and Srivastava (1986) had developed a competitor test to the usual t-test by using the Jackknife estimator of the common population variance. This test can be used as an alternative to the Behrens – Fisher problem. In this paper powers of two commonly used tests, Welch – Satterthwaite test and Cochran – Cox test, have been compared to Saxena – Srivastava test empirically.

Key Words and Phrases:

• Behrens-Fisher problem
• Student's t-distribution
• power comparison
• unequal variance