Abstract #300196

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JSM 2003 Abstract #300196
Activity Number: 338
Type: Contributed
Date/Time: Wednesday, August 6, 2003 : 8:30 AM to 10:20 AM
Sponsor: Section on Statistical Education
Abstract - #300196
Title: Two-Sample Tests of Means: Going Back on Welch?
Author(s): David P. Doane*+
Companies: Oakland University
Address: 173 Tartan, Rochester Hills, MI, 48309-1810,
Keywords: Welch ; Behrens-Fisher ; power ; two means ; pooled variance
Abstract:

When population variances are unequal, Welch's test in a two-sample test of means will reduce Type I error compared to a pooled-variance t-test, and that Welch's test is asymptotically uniformly most powerful among one-tailed alternatives. Yet many applied introductory textbooks omit Welch's test, perhaps because of its computational complexity and/or the expectation that in large samples it will not matter. Do those who rely on such textbooks actually face a greater risk of error? This paper (1) surveys the advice offered by introductory textbooks; (2) uses simulation to explore empirical Type I and II error over a range of sample sizes, population variances, and differences of means; and (3) evaluates rules of thumb that might alert a decisionmaker to situations where Welch's test is needed. We find that, while simple rules of thumb provide only limited guidance, the risk of always using a pooled t-test appears modest.

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