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Conditions for the Effectiveness of a Preliminary Test of Variance

Carol A. Markowski and Edward P. Markowski
The American Statistician
Vol. 44, No. 4 (Nov., 1990), pp. 322-326
DOI: 10.2307/2684360
Stable URL: http://www.jstor.org/stable/2684360
Page Count: 5
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Conditions for the Effectiveness of a Preliminary Test of Variance
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Abstract

We evaluate the performance of the F test for the equality of two variances as a preliminary test to determine the appropriateness of the two-sample t test. When sampling is from a normal distribution, our results indicate that, for equal sample sizes, the t test is insensitive to variance heterogeneity and hence no preliminary test is necessary. For unequal sample sizes, the F test has small probability of detecting many alternatives for which the t test performs poorly, and so the F test is not an effective preliminary test. When sampling is from other distributions, our results confirm the sensitivity of the F test to the normality assumption.

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