USING AN APPROXIMATE CHI-SQUARE STATISTIC TO TEST THE NUMBER OF DIMENSIONS UNDERLYING THE RESPONSES TO A SET OF ITEMS

An approximate chi(2) statistic based on McDonald's (1967) nonlinear f actor analytic representation of item response theory was proposed and investigated with simulated data. The results were compared with Stou t's T statistic (Nandakumar & Stout, 1993; Stout, 1987). Unidimensiona l and two-dimensional item response data were simulated under varying levels of sample size, test length, test reliability, and dimension do minance. The approximate chi(2) statistic had good control over Type I errors when unidimensional data were generated and displayed very goo d power in identifying the two-dimensional data. The performance of th e approximate chi(2) was at least as good as Stout's T statistic in al l conditions and was better than Stout's T statistic with smaller samp le sizes and shorter tests. Further implications regarding the potenti al use of nonlinear factor analysis and the approximate chi(2) in addr essing current measurement issues are discussed.