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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.
Robert A. Smith (1971) studied this question.