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Four New Corrected Statistics for Structural Equation Modeling with Small Sample and Nonnormally Distributed Data

The likelihood ratio statistic, TML, is the most widely used statistic for evaluating structural equation modeling (SEM) models. With nonnormally distributed data, referring TML to its nominal chi-square distribution can be misleading (Yuan & Bentler, 1998). The mean rescaled statistic, TRML, and the mean-and-variance-adjusted statistic, TAML, which are proposed to account for nonnormally distributed data (Satorra & Bentler, 1994), require medium to large sample size N to maintain reasonable Type I error control (Nevitt & Hancock, 2004; Savalei, 2010). This study proposed and investigated four new statistics for nonnormally distributed data with small N. The first three correct either TRML or TAML for