In this study, the Canadian English and French versions of the Problem-Solving Measure of the Programme for International Student Assessment 2003 were examined to investigate their degree of measurement comparability at the item- and test-levels. Three methods of differential item functioning (DIF) were compared: parametric and nonparametric item response theory and ordinal logistic regression. Corresponding derivations of these three DIF methods were investigated at the test-level to examine both differential test functioning (DTF) and the correspondence between findings at the item-level with those at the test-level. Item-level findings suggested consistency in DIF detection across methods; however, differences in effect sizes of DIF were found by each method. Test-level results revealed a high degree of consistency across DTF methods. Discrepancies were found between item- and test-level comparability analyses. Item-level analyses suggested moderate to low degrees of comparability, whereas test-level findings suggested a higher degree of comparability. Findings also indicated the direction of DIF was mixed as some DIF items favored English-speaking students and others favored French-speaking students, suggesting that DIF cancellation may explain why item-level incomparability was not detected at the test-level.
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Oliveri et al. (2012) studied this question.