The empirical Type I error rates of Poly-DIMTEST (H. Li and W. Stout, 1995) and the LISREL8 chi square fit statistic (K. Joreskog and D. Sorbom, 1993) were compared with polytomous unidimensional data sets simulated to vary as a function of test length and sample size. The rejection rates for both statistics were also studied with two-dimensional data sets simulated to vary as a function of test length, sample size, and degree of correlation between latent traits. Severely inflated Type I error rates were obtained with the LISREL8 chi square statistic in all conditions, with the exception of the 10-item data sets simulated to contain 500 and 1,000 simulees. Poly-DIMTEST T-empirical Type I error probabilities were at or near nominal values for the three sample sizes examined. In addition, the performance of the latter statistic was unaffected by the manipulation of sample size. Rejection rates using the LISREL8 chi square fit statistic were high across all simulated two-dimensional conditions, although results were encouraging for 10-item data sets containing 500 or 1,000 simulees. It appeared that neither procedure worked well with samples of less than 500 examinees. Results do suggest that with samples of 500 examinees or more, the LISREL8 chi square statistic can be useful for assessment of dimensionality, but the Poly-DIMTEST T-statistic lacks the power needed to use with samples of fewer than 20 items. (Contains 3 tables and 38 references.) (SLD)