This article concerns the simultaneous assessment of DIF for a collection of test items. Rather than an average or sum in which positive and negative DIF may cancel, we propose an index that measures the variance of DIF on a test as an indicator of the degree to which different items show DIF in different directions. It is computed from standard Mantel‐Haenszel statistics (the logodds ratio and its variance error) and may be conceptually classified as a variance component or variance effect size. Evaluated by simulation under three item response models (IPL, 2PL, and 3PL), the index is shown to be an accurate estimate of the DTF generating parameter in the case of the 1PL and 2PL models with groups of equal ability. For groups of unequal ability, the index is accurate under the I PL but not the 2PL condition; however, a weighted version of the index provides improved estimates. For the 3PL condition, the DTF generating parameter is underestimated. This latter result is due in part to a mismatch in the scales of the log‐odds ratio and IRT difficulty.
Two forms of a c-sample normal scores test are presented as alternatives to the Kruskal-Wallis test (KW). The normal scores test statistics and multiple comparison procedures are illustrated for large samples requiring a correction for tied observations. Theoretical and empirical evidence is cited in support of using the normal scores test in preference to a rank test such as the KW. The normal scores test is asymptotically more efficient than the KW for samples from common non-normal populations (e.g. uniform and exponential) and is less sensitive to nan-normality and unequal variances than is either the F-test or the KW test.
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