According to Kenny and McCoach (2003), chi-square tests of structural equation models produce inflated Type I error rates when the degrees of freedom increase. So far, the amount of this bias in large models has not been quantified. In a Monte Carlo study of confirmatory factor models with a range of 48 to 960 degrees of freedom it was found that the traditional maximum likelihood ratio statistic, T[subscript ML], overestimates nominal Type I error rates up to 70% under conditions of multivariate normality. Some alternative statistics for the correction of model-size effects were also investigated: the scaled Satorra-Bentler statistic, T[subscript SC]; the adjusted Satorra-Bentler statistic, T[subscript AD] (Satorra & Bentler, 1988, 1994); corresponding Bartlett corrections, T[subscript MLb], T[subscript SCb], and T[subscript ADb] (Bartlett, 1950); and corresponding Swain corrections, T[subscript MLs], T[subscript SCs], and T[subscript ADs] (Swain, 1975). The empirical findings indicate that the model test statistic TMLs should be applied when large structural equation models are analyzed and the observed variables have (approximately) a multivariate normal distribution.