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Estimation of parameters for the many-facets Rasch model requires that conditional on the values of the facets, such as person ability, item difficulty, and rater severity, the observed responses within each facet are independent. This requirement has often been discussed for the Rasch models and 2PL and 3PL models, but it becomes more complex with more facets. To show how violation of conditional independence may be exhibited, three scenarios with different types of dependency are developed: (1) raters rating the same work; (2) a residual ability shared by two tasks; and (3) score on one task dependent on observed score on a previous task.

Three types of effects sizes for DIF are described in this exposition: log of the odds-ratio (differences in log-odds), differences in probability-correct, and proportion of variance accounted for. Using these indices involves conceptualizing the degree of DIF in different ways. This integrative review discusses how these measures are impacted in different ways by item difficulty, item discrimination, and item lower asymptote. For example, for a fixed discrimination, the difference in probabilities decreases as the difference between the item difficulty and the mean ability increases. Under the same conditions, the log of the odds-ratio remains constant if the lower asymptote is zero. A non-zero lower asymptote decreases the absolute value of the probability difference symmetrically for easy and hard items, but it decreases the absolute value of the log-odds difference much more for difficult items. Thus, one cannot set a criterion for defining a large effect size in one metric and find a corresponding criterion in another metric that is equivalent across all items or ability distributions. In choosing an effect size, these differences must be understood and considered. (Contains 2 tables, 6 footnotes, and 7 figures.)

Three methods of detecting item drift were compared: the procedure in BILOG-MG for estimating linear trends in item difficulty, the CUSUM procedure that Veerkamp and Glas (2000) used to detect trends in difficulty or discrimination, and a modification of Kim, Cohen, and Park's (1995) x 2 test for multiple-group differential item functioning (DIF), using linear contrasts on the discrimination and difficulty parameters. Data were simulated as if collected over 3, 4, or 5 time points, with parameter drift in either a gradual, linear pattern, a less linear but still monotonic pattern, or as a sudden shift at the third time point. The BILOG-MG procedure and the modification of the Kim et al. procedure were more powerful than the CUSUM procedure, nearly always detecting drift. All three procedures had false alarm rates for nondrift items near the nominal alpha. The procedures were also illustrated on a real data set.

Studied the effects of test consequences, response formats, gender, and ethnicity on the mathematics and science sections of the Michigan High School Proficiency Test. Results for more than 11,000 students show that students taking constructed response and multiple choice formats performed better under high stakes conditions. Discusses gender and ethnic differences. (SLD)

Scores from mathematics (tested at 102 schools) and science (tested at 99 schools) sections of pilot forms of the Michigan High School Proficiency Test were examined for interaction between gender and response format (multiple choice or constructed response). Overall, neither males nor females seemed to be disadvantaged by item format. (SLD)