Pairwise Multiple Comparisons in the Homogeneous Variance, Unequal Sample Size Case

The effect of unequal n i on the error rates of six procedures for pair-wise multiple comparisons beteen k treatment means with homogeneous variances was studied by computer simulation. A commonly used method, attributed to Kramer (1956) but suggested also by Tukey (1953), was found to have error ra...

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Bibliographic Details
Published in:Journal of the American Statistical Association 1980-12, Vol.75 (372), p.789-795
Main Author: Dunnett, Charles W.
Format: Article
Language:English
Subjects:
Applications
Approximation
Computer simulation
Duncan method
Error rates
Harmonic mean
Multiple comparisons
Multiple range tests
Newman-Keuls test
Probabilities
Sample size
Standard error
Statistical discrepancies
Statistical variance
Test ranges
Tukey method
Unequal sample size
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Summary:The effect of unequal n i on the error rates of six procedures for pair-wise multiple comparisons beteen k treatment means with homogeneous variances was studied by computer simulation. A commonly used method, attributed to Kramer (1956) but suggested also by Tukey (1953), was found to have error rates less than the nominal value α for several patterns of inequality in the sample sizes, at least when the variations in n i were moderately large. A method that substitutes the harmonic mean sample size for n in Tukey's T method had excessively high error rates. Other methods proposed more recently in the literature were conservative relative to the Tukey-Kramer method. Thus, the Tukey-Kramer method is recommended for use in the unequal sample size, homogeneous variance situation.
ISSN:0162-1459
1537-274X
DOI:10.1080/01621459.1980.10477551