Exact Solutions to the Behrens-Fisher Problem: Asymptotically Optimal and Finite Sample Efficient Choice Among the Solutions due to Chapman, to Prokof'yev and Shishkin, and to Dudewicz and Ahmed
by
Edward J. Dudewicz
Dept. of Mathematics, Syracuse University, 215 Carnegie Hall, Syracuse, New York 12344-1150
Coauthors: Yan Ma, Shirley Enping Mai, Haiyan Su

The problem of testing the equality of two normal means when variances are not known is called the Behrens-Fisher Problem. This problem has three known exact solutions, due respectively to Chapman, to Prokof'yev and Shishkin, and to Dudewicz and Ahmed. Each procedure has level alpha and power beta when the means differ by a given amount delta, both set by the experimenter. No single-sample statistical procedures can make this guarantee. The most recent of the three procedures is asymptotically optimal. We review the procedures, and then compare them with respect to both asymptotic efficiency and also (using simulation) in finite samples. One of these exact procedures is recommended for practical use.

Date received: June 9, 2003