Sankhya: The Indian Journal of Statistics

2002, Volume 64, Series A, Pt. 1, pp. 139--155

A SIMPLE CONSERVATIVE AND ROBUST SOLUTION OF THE BEHRENS-FISHER PROBLEM

By

HAROLD RUBEN, Epping, Essex, U.K.

SUMMARY. A basic and elementary geometrical proposition is used to provide a solution of the Behrens-Fisher problem which is both conservative and robust. An explicit formula is given which allows a strict upper bound of p to be obtained and also allows confidence intervals of the difference in population means to be computed with confidence coefficient strictly greater than 1-alpha. (alpha is a prescribed small positive constant). The main results of this paper are given by (Ia),(Ib), (Ic), (Id) together with (II), in Section 2, and (III) is Section 3.

AMS (1991) subject classification. 62F03, 62F25.

Key words and phrases. Behrens-Fisher problem, geometrical proposition, conservative and robust, strict upper bound for p, conditional and unconditional pivotals, tail probabilities.

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