Hostname: page-component-745bb68f8f-v2bm5 Total loading time: 0 Render date: 2025-01-07T19:00:13.497Z Has data issue: false hasContentIssue false
  • English
  • Français

The Effect of Unequal Group Size on Tukey's HSD Procedure

Published online by Cambridge University Press:  01 January 2025

Robert A. Smith
Robert A. Smith*
Affiliation:
University of Colorado
Get access Rights & Permissions [Opens in a new window]

Abstract

A limitation of the Tukey HSD procedure for multiple comparison has been the requirement of equal number of observations for each group. Three approximation techniques have been suggested when the group sizes are unequal. Each of these techniques was empirically analyzed to determine its effect on Type I error. Two of the considered variables, average group size and differences in group size, caused differing actual probabilities of Type I error. One of the three techniques (Kramer's) consistently provided actual probabilities in close agreement with corresponding nominal probabilities.

Keywords

Public PolicyGroup SizeStatistical TheoryAverage GroupClose Agreement
Type
Original Paper
Information
Psychometrika , Volume 36 , Issue 1 , March 1971 , pp. 31 - 34
Copyright
Copyright © 1971 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

*

Now at the University of Southern California.

References

Harter, H. L., & Clemm, D. S., Guthrie, E. H. The probability integrals of the range and of the studentized range, 1959, Washington: U. S. Department of CommerceGoogle Scholar
Hays, W. Statistics for psychologists, 1963, New York: Holt, Rinehart & WinstonGoogle Scholar
Kramer, C. Y. Extension of multiple range test to group means with unequal numbers of replications. Biometrics, 1956, 12, 307–310CrossRefGoogle Scholar
Miller, R. G. Jr. Simultaneous statistical inference, 1966, New York: McGraw-HillGoogle Scholar
Myers, J. L. Fundamentals of experimental design, 1966, Boston: Allyn & BaconGoogle Scholar
Parzen, E. Modern probability theory and its applications, 1960, New York: WileyCrossRefGoogle Scholar
Ryan, T. A. Multiple comparisons in psychological research. Psychological Bulletin, 1959, 56, 26–47CrossRefGoogle ScholarPubMed
Scheffé, H. The analysis of variance, 1959, New York: WileyGoogle Scholar
Steel, R. G. D., & Torrie, J. H.. Principles and procedures of statistics, 1960, New York: McGraw-HillGoogle Scholar
Winer, B. J. Statistical principles in experimental design, 1962, New York: McGraw-HillCrossRefGoogle Scholar