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Some Tests for Variance Components Using Generalized p Values

Leping Zhou and Thomas Mathew
Technometrics
Vol. 36, No. 4 (Nov., 1994), pp. 394-402
DOI: 10.2307/1269954
Stable URL: http://www.jstor.org/stable/1269954
Page Count: 9
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Some Tests for Variance Components Using Generalized p Values
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Abstract

The concept of a generalized p value, introduced by Tsui and Weerahandi, is applied for testing hypotheses in two situations, testing the significance of a variance component in a general balanced mixed model when an exact F test does not exist and comparing random-effects variance components in two independent balanced mixed models. Extensions to the unbalanced cases are also indicated. The proposed test is compared with the test based on the Satterthwaite approximation through their simulated Type I error probabilities. The simulations indicate that the test based on the generalized p value has Type I error probabilities less than the chosen significance level most of the time, whereas the Type I error probabilities of the Satterthwaite approximate test can be much larger than the significance level. The results are illustrated using two examples.

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