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On the Behrens-Fisher Problem: A Review

The University of Georgia

Allan S. Cohen

University of Wisconsin-Madison

The Behrens-Fisher problem arises when one seeks to make inferences about the means of two normal populations without assuming the variances are equal. This paper presents a review of fundamental concepts and applications used to address the Behrens-Fisher problem under fiducial, Bayesian, and frequentist approaches. Methods of approximations to the Behrens-Fisher distribution and a simple Bayesian framework for hypothesis testing are also discussed. Finally, a discussion is provided for the use of generalized p values in significance testing of hypotheses in the presence of nuisance parameters. It is shown that the generalized p values based on a frequentist probability for the Behrens-Fisher problem are numerically the same as those from the fiducial and Bayesian solutions. A table for tests of significance is also included.

Key Words: Keywords: Behrens-Fisher problem • two means problem • unequal variances

Journal of Educational and Behavioral Statistics, Vol. 23, No. 4, 356-377 (1998)
DOI: 10.3102/10769986023004356


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