A Bias-Corrected Test Statistic for Confirmatory Factor Analysis Under Non-Normality

Confirmatory factor analysis relies on multivariate normality, yet violations frequently compromise Type I error control. This study develops ridge-calibrated test statistics integrating bias corrections refined through Monte Carlo simulation. Evaluation of eleven methods across twelve distributional conditions and nine sample size configurations (108,000 replications; p = 12–24, n = 60–180) shows TFCr achieves Type I error rates of 0.036, within Bradley’s liberal criterion [0.025, 0.075]. In contrast, ML chi-square shows 0.251, Satorra-Bentler 0.172, and Foldnes F2 0.148. Correction effectiveness remains stable (84.5%–85.9%) across violation types, from mild skewness to severe contamination. Applications to Holzinger-Swineford (n = 301) and Political Democracy (n = 75) datasets demonstrate 8.5%–11.9% chi-square reductions with improved fit indices. TFCr maintains consistent performance across distributional conditions, while TCsFCr shows variable effectiveness (91.5% mean reduction), reflecting Satorra-Bentler scaling’s sensitivity to kurtosis. Results suggest ridge-calibrated corrections provide improved Type I error control under conditions examined.