Tucker's congruence coefficient is often used to compare the equality of latent structures on a given test for different subgroups. Initial use of the index was subjective; given the same congruence coefficient, one investigator could decide that a pair of factors was similar, whereas another investigator could decide that they were different. Critical values were subsequently developed for this index to provide an objective basis for decision making. In practice, these values too often suggest congruence between factors known to differ. Results of the present study suggest that significance tests of congruence coefficients are inappropriate as currently performed.
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