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Mantel-Haenszel methods comprise a highly flexible methodology for assessing the degree of association between two categorical variables, whether they are nominal or ordinal, while controlling for other variables. The versatility of Mantel-Haenszel analytical approaches has made them very popular in the assessment of the differential functioning of both dichotomous and polytomous items. Up to now, researchers have limited the use of Mantel-Haenszel statistics to analyzing contingency tables of dimensions 2 × 2 (by means of the Mantel-Haenszel chi-square statistic) and of dimensions of 2 × C (by means of either the generalized Mantel-Haenszel test or Mantel's test). The main objective of this article is to illustrate a unified framework for the analysis of differential item functioning using the Mantel-Haenszel methods. This is done by means of the generalized Mantel-Haenszel statistic for the analysis of the general case of Q contingency tables with dimensions R × C. Moreover, with the new formulation in consideration, this article reviews the most recent research on differential item functioning and suggests new applications and research lines in relation to the statistics proposed.

This article examines whether there are gender differences in understanding the emotions evaluated by the Test of Emotion Comprehension (TEC). The TEC provides a global index of emotion comprehension in children 3–11 years of age, which is the sum of the nine components that constitute emotion comprehension: (1) recognition of facial expressions, (2) understanding of external causes of emotions, (3) understanding of desire-based emotions, (4) understanding of belief-based emotions, (5) understanding of the influence of a reminder on present emotional states, (6) understanding of the possibility to regulate emotional states, (7) understanding of the possibility of hiding emotional states, (8) understanding of mixed emotions, and (9) understanding of moral emotions. We used the answers to the TEC given by 172 English girls and 181 boys from 3 to 8 years of age. First, the nine components into which the TEC is subdivided were analysed for differential item functioning (DIF), taking gender as the grouping variable. To evaluate DIF, the Mantel–Haenszel method and logistic regression analysis were used applying the Educational Testing Service DIF classification criteria. The results show that the TEC did not display gender DIF. Second, when absence of DIF had been corroborated, it was analysed for differences between boys and girls in the total TEC score and its components controlling for age. Our data are compatible with the hypothesis of independence between gender and level of comprehension in 8 of the 9 components of the TEC. Several hypotheses are discussed that could explain the differences found between boys and girls in the belief component. Given that the Belief component is basically a false belief task, the differences found seem to support findings in the literature indicating that girls perform better on this task

Empirical Type I error and power rates were estimated for (a) the doubly multivariate model, (b) the Welch-James multivariate solution developed by Keselman, Carriere and Lix (1993) using Johansen's results (1980), and for (c) the multivariate version of the modified Brown-Forsythe (1974) procedure. The performance of these procedures was investigated by testing within-blocks sources of variation in a multivariate split-plot design containing unequal covariance matrices. The results indicate that the doubly multivariate model did not provide effective Type I error control while the Welch-James procedure provided robust and powerful tests of the within-subjects main effect, however, this approach provided liberal tests of the interaction effect. The results also indicate that the modified Brown-Forsythe procedure provided robust tests of within-subjects main and interaction effects, especially when the design was balanced or when group sizes and covariance matrices were positively paired.

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