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Welch's Approximate Solution for the Behrens-Fisher Problem

D. J. Best and J. C. W. Rayner
Technometrics
Vol. 29, No. 2 (May, 1987), pp. 205-210
DOI: 10.2307/1269775
Stable URL: http://www.jstor.org/stable/1269775
Page Count: 6
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Welch's Approximate Solution for the Behrens-Fisher Problem
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Abstract

The Wald, likelihood ratio, and score statistics have been calculated for the Behrens-Fisher problem. These statistics provide asymptotically equivalent and weakly optimal tests. The test based on the Wald statistic was found to be very similar to the V test discussed by Welch (1937); hence the V test was compared with the likelihood ratio and score tests in a power study. Since the powers were very similar and the V test was more convenient to use from several points of view, we recommend this test. Sizes of the V test, as well as a power comparison with the usual pooled t test, were also obtained.

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