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Biometrika 1974 61(1):117-122; doi:10.1093/biomet/61.1.117
© 1974 by Biometrika Trust
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The harmonic mean method for one-way and two-way analyses of variance

NEIL O. RANKIN

Department of Psychology, Clark University Worcester, Massachusetts

This paper investigates the properties of the harmonic mean method for the analysis of variance with unequal sample sizes for one- and two-way classifications. The test statistic is shown to be distributed as a ratio of linear combinations of chi-squared random variables. Under the null hypothesis, this distribution may be approximated by a central F distribution with the degrees of freedom of the numerator adjusted in accordance with the discrepancies in the sample size. Simulation methods are used to show that the approximation is accurate over a range of conditions and that the test based on least squares is not uniformly more powerful than the test based on the harmonic mean procedure.

Key Words: Analysis of variance with unequal sample sizes • Harmonic mean method • Unweighted means analysis


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