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

E. Kulinskaya; R. G. Staudte; H. Gao

doi:10.1081/STA-120025383

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

E. Kulinskaya, R. G. Staudte, H. Gao

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19 Citations (Scopus)

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.

Original language	English
Pages (from-to)	2353-2371
Number of pages	19
Journal	Communications in Statistics: Theory and Methods
Volume	32
Issue number	12
DOIs	https://doi.org/10.1081/STA-120025383
Publication status	Published - 2003

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10.1081/STA-120025383

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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.",

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AU - Staudte, R. G.

AU - Gao, H.

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AB - 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.

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JO - Communications in Statistics: Theory and Methods

JF - Communications in Statistics: Theory and Methods

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