The problem of this study was to determine the differences in experimentwise and comparisonwise Type I error rate among six multiple comparison procedures when applied to twenty-eight combinations of normally distributed data. These were the Least Significant Difference, the Fisher-protected Least Significant Difference, the Student Newman-Keuls Test, the Duncan Multiple Range Test, the Tukey Honestly Significant Difference, and the Scheffe Significant Difference. The Spjøtvoll-Stoline and Tukey—Kramer HSD modifications were used for unequal n conditions. A Monte Carlo simulation was used for twenty-eight combinations of k and n. The scores were normally distributed (µ=100; σ=10). Specified multiple comparison procedures were applied under two conditions: (a) all experiments and (b) experiments in which the F-ratio was significant (0.05). Error counts were maintained over 1000 repetitions. The FLSD held experimentwise Type I error rate to nominal alpha for the complete null hypothesis. The FLSD was more sensitive to sample mean differences than the HSD while protecting against experimentwise error. The unprotected LSD was the only procedure to yield comparisonwise Type I error rate at nominal alpha. The SNK and MRT error rates fell between the FLSD and HSD rates. The SSD error rate was the most conservative. Use of the harmonic mean of the two unequal sample n's (HSD-TK) yielded uniformly better results than use of the minimum n (HSD-SS). Bernhardson's formulas controlled the experimentwise Type I error rate of the LSD and MRT to nominal alpha, but pushed the HSD below the 0.95 confidence interval. Use of the unprotected HSD produced fewer significant departures from nominal alpha. The formulas had no effect on the SSD.

The central theme of this thesis is the construction of simultaneous confidence regions (SCR) corresponding to stepwise multiple comparison procedures (MCP). The first chapter is devoted to the theory of multiple comparisons, including the class of closed testing procedures which contains every MCP that strongly con- trols the familywise error rate. The second chapter is concerned with the gene- ral principle of construction of SCR corresponding to closed testing procedures. These general results are used in the third and the forth chapter for deriving the SCR corresponding to a subclass of closed testing procedures which are based on weighted Bonferroni tests. The SCR corresponding to the Holm, the Holm(W), the fixed-sequence and the fallback MCP are derived explicitly. The theoretical results are numerically illustrated on a bioequivalence study. In the fifth chapter we briefly discuss the SCR corresponding to the Hommel, the Hochberg and the step-down Dunnett MCP.

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