The problem of this study was to examine the equivalency of two different types of criterion-referenced item-selection techniques on simulated data as item pools varied in degrees of item difficulty. A pretest-posttest design was employed in which pass-fail scores were randomly generated for item pools of twenty-five items. From the item pools, the two techniques determined which items were to be used to make up twelve-item criterion-referenced tests. The twenty-five items also were rank ordered according to the discrimination power of the two techniques.

This study sought to determine the effect upon Tukey's Honestly Significant Difference (HSD) statistic of concurrently violating the assumptions of homogeneity of variance and equal sample sizes. Two forms for the unequal sample size problem were investigated. Kramer's form and the harmonic mean approach were the two unequal sample size procedures studied. The study employed a Monte Carlo simulation procedure which varied sample sizes with a heterogeneity of variance condition. Four thousand experiments were generated. Findings of this study were based upon the empirically obtained significance levels. Five conclusions were reached in this study. The first conclusion was that for the conditions of this study the Kramer form of the HSD statistic is not robust at the .05 or .01 nominal level of significance. A second conclusion was that the harmonic mean form of the HSD statistic is not robust at the .05 and .01 nominal level of significance. A general conclusion reached from all the findings formed the third conclusion. It was that the Kramer form of the HSD test is the preferred procedure under combined assumption violations of variance heterogeneity and unequal sample sizes. Two additional conclusions are based on related findings. The fourth conclusion was that for …