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An approximate χ 2 statistic based on McDonald's (1967) nonlinear factor analytic representation of item response theory was proposed and investigated with simulated data. The results were compared with Stout's T statistic (Nandakumar & Stout, 1993; Stout, 1987). Unidimensional and two‐dimensional item response data were simulated under varying levels of sample size, test length, test reliability, and dimension dominance. The approximate χ 2 statistic had good control over Type I errors when unidimensional data were generated and displayed very good power in identifying the two‐dimensional data. The performance of the approximate χ 2 was at least as good as Stout's T statistic in all conditions and was better than Stout's T statistic with smaller sample sizes and shorter tests. Further implications regarding the potential use of nonlinear factor analysis and the approximate χ 2 in addressing current measurement issues are discussed.
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Gessaroli et al. (1996) studied this question.
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