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 TypeI error. Two of the considered variables, average group size and differences in group size, caused differing actual probabilities of TypeI error. One of the three techniques (Kramer's) consistently provided actual probabilities in close agreement with corresponding nominal probabilities.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Harter, H. L., Clemm, D. S., & Guthrie, E. H.The probability integrals of the range and of the studentized range. Washington: U. S. Department of Commerce, 1959.
Hays, W.Statistics for psychologists. New York: Holt, Rinehart & Winston, 1963.
Kramer, C. Y. Extension of multiple range test to group means with unequal numbers of replications.Biometrics, 1956,12, 307–310.
Miller, R. G., Jr.Simultaneous statistical inference. New York: McGraw-Hill, 1966.
Myers, J. L.Fundamentals of experimental design. Boston: Allyn & Bacon, 1966.
Parzen, E.Modern probability theory and its applications. New York: Wiley, 1960.
Ryan, T. A. Multiple comparisons in psychological research.Psychological Bulletin, 1959,56, 26–47.
Scheffé, H.The analysis of variance. New York: Wiley, 1959.
Steel, R. G. D. & Torrie, J. H.Principles and procedures of statistics. New York: McGraw-Hill, 1960.
Winer, B. J.Statistical principles in experimental design. New York: McGraw-Hill, 1962.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Smith, R.A. The effect of unequal group size on Tukey's HSD procedure. Psychometrika 36, 31–34 (1971). https://doi.org/10.1007/BF02291420
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02291420