An Evaluation of Two Unequal nk Forms of the Tukey Multiple Comparison Statistic

Abstract The harmonic mean and Kramer [13] unequal nk forms of the Tukey multiple comparison test were compared for observed Type I error and correct decision rates. Sensitivity was evaluated under the restriction that the analysis of variance F-test be significant at α = 0.05, under numerous parametric specifications which represent behavioral research data. The data indicates that both procedures are adversely affected by combining unequal variances with unequal sample sizes and have the same sensitivity for detecting real mean differences.

[1]  H. Keselman,et al.  Effect of Very Unequal Group Sizes On Tukey's Multiple Comparison Test , 1976 .

[2]  K. Gabriel,et al.  A Study of the Powers of Several Methods of Multiple Comparisons , 1975 .

[3]  Gary C. Ramseyer,et al.  The Robustness of the Studentized Range Statistic to Violations of the Normality and Homogeneity of Variance Assumptions , 1973 .

[4]  S. G. Carmer,et al.  An Evaluation of Ten Pairwise Multiple Comparison Procedures by Monte Carlo Methods , 1973 .

[5]  Robert A. Smith,et al.  The effect of unequal group size on Tukey's HSD procedure , 1971 .

[6]  T. Donaldson.  Robustness of the F-Test to Errors of Both Kinds and the Correlation Between the Numerator and Denominator of the F-Ratio , 1968 .

[7]  William F. Massy,et al.  Multivariate Procedures for the Behavioral Sciences. , 1964 .

[8]  Seymour Geisser,et al.  Statistical Principles in Experimental Design , 1963 .

[9]  F. N. David,et al.  Principles and procedures of statistics. , 1961 .

[10]  R. L. Plackett,et al.  The Analysis of Variance , 1960 .

[11]  M. E. Muller,et al.  A Note on the Generation of Random Normal Deviates , 1958 .

[12]  Clyde Young Kramer,et al.  Extension of multiple range tests to group means with unequal numbers of replications , 1956 .

[13]  G. Box.  Some Theorems on Quadratic Forms Applied in the Study of Analysis of Variance Problems, I. Effect of Inequality of Variance in the One-Way Classification , 1954 .

[14]  H. Keselman,et al.  Tukey tests for pair-wise contrasts following the analysis of variance: Is there a type IV error? , 1974 .

[15]  G. Glass,et al.  Statistical methods in education and psychology , 1970 .

[16]  R. Kirk.  Experimental Design: Procedures for the Behavioral Sciences , 1969 .

[17]  Curtis Hardyck,et al.  Error rates for multiple comparison methods: Some evidence concerning the frequency of erroneous conclusions. , 1969 .