EFFECT OF THE ABILITY DISTRIBUTION SHAPE ON THE GENERALIZED MANTEL-HAENSZEL STATISTICS USED FOR DIF DETECTION

The main objective of this simulation study was to explore the effect of shape of the θ distribution on the generalized nominal and ordinal Mantel-Haenszel statistics used for detecting DIF in polytomous items. The variables manipulated were: trait ( θ), distribution shape (normal, positively skewed, and platykurtic), θ distribution difference between the reference and the focal group (equal and unequal), sample size (500/ 500 and 500/250 examinees in the reference/focal group), and DIF conditions (No DIF, constant and shift-high DIF patterns). The generalized ordinal Mantel-Haenszel statistic was calculated using integer and log-rank scores. The results show: a) a little impact of the θ distribution shape on the performance of all the statistics, and b) the advantages of employing log-rank scores, especially when the items show a shift-high DIF pattern.

A Modified Maximum Contrast Method for Unequal Sample Sizes in Pharmacogenomic Studies

In pharmacogenomic studies, biomedical researchers commonly analyze the association between genotype and biological response by using the Kruskal-Wallis test or one-way analysis of variance (ANOVA) after logarithmic transformation of the obtained data. However, because these methods detect unexpected biological response patterns, the power for detecting the expected pattern is reduced. Previously, we proposed a combination of the maximum contrast method and the permuted modified maximum contrast method for unequal sample size in pharmacogenomic studies. However, we noted that the distribution of the permuted modified maximum contrast statistic depends on nuisance parameter σ2, which is the population variance. In this paper, we propose a modified maximum contrast method with a statistic that does not depend on the nuisance parameter. Furthermore, we compare the performance of these methods via simulation studies. The simulation results showed that the modified maximum contrast method gave the lowest false-positive rate; therefore, this method is powerful for detecting the true response patterns in some conditions. Further, it is faster and more accurate than the permuted modified maximum contrast method. On the basis of these results, we suggest a rule of thumb to select the appropriate method in a given situation.