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.