Four multidimensional data configurations and one unidimensional data configuration were simulated for three differences in mean difficulty between two tests to be equated. Two chi-square statistics, Q1 and Q2, were examined for their ability to detect multidimensionality. Results indicated that Q1 did not discriminate between any of the multidimensional configurations, nor did it discriminate any of the multidimensional conditions from any of the unidimensional conditions. The other chi-square statistic, Q2, overwhelmingly detected all three conditions of one of the four multidimensional configurations. Both horizontal and vertical equatings for the multidimensional configurations were as good as those for the unidimensional configurations when correlations were examined. When means were examined, the multidimensional tests usually had worse equatings than the unidimensional tests, particularly when the tests differed in difficulty. (Author)