Power approximations in testing for unequal means in a one-way ANOVA weighted for unequal variances

Kulinskaya, E., Staudte, R. G. and Gao, H. (2003) Power approximations in testing for unequal means in a one-way ANOVA weighted for unequal variances. Communications in Statistics: Theory and Methods, 32 (12). pp. 2353-2371. ISSN 0361-0926

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Abstract

The classical F-test for unequal means in a one-way ANOVA is known to be misleading when the populations have different variances. To overcome this (James, G. S. (1951). The comparison of several groups of observations when the ratios of the population variances are unknown. Biometrika 38:324–329 and Welch, B. L. (1951). On the comparison of several mean values: an alternative approach. Biometrika 38:330–336.) weighted the terms in the numerator sum of squares by the respective inverses of the sample mean variances, and they proposed equivalent tests based on F or ? 2 approximations to the null distribution of the weighted sum of squares for moderate sample sizes. We provide approximations for the nonnull distributions of their weighted statistics which are found to be useful in obtaining approximations to the power of the Welch F-test.

Item Type: Article
Faculty \ School: Faculty of Science > School of Computing Sciences
Related URLs:
Depositing User: Vishal Gautam
Date Deposited: 23 Jul 2011 17:43
Last Modified: 13 Mar 2019 14:32
URI: https://ueaeprints.uea.ac.uk/id/eprint/23601
DOI: 10.1081/STA-120025383

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