Unidimensionality versus statistical accuracy: A note on Bejar's method for detecting dimensionality of achievement tests

Abstract

A simulation investigated use of the difficulty parameter (Bejar, 1980) to evaluate item unidimensionality. Artificial tests were designed to be nonequivalent in both length and dimensionality. Simulated item responses to the tests were analyzed with the LOGIST computer program. Two indices were calculated: the slope of the principal axis between the content-areabased item difficulty estimates and corresponding total- test-based estimates, and the correlation between the two sets of estimates. Results show that the magnitude of the correlation coefficient provides no information about dimensionality of a set of test items. The slope of the principal axis, on the other hand, is sensitive to multidimensionality in the data as well as test length. The size of the slope adequately detects the dimensionality of items for relatively long tests. Index terms: equating, item difficulty parameters, item response theory, unidimensionality.