The purpose of the paper is to investigate the performance of method of estimation, WLS, under small sample sizes. In this investigation we use Monte Carlo simulation to generate pseudo data under factorial design given different specified CFA models. Results show that the parameter estimation of WLS is not precise enough. The smaller the sample sizes are, the less precise the estimation is. Moreover, in the model evaluation WLS is prone to resulting in type I error. These findings enrich the understanding of the small sample properties of WLS on CFA model. Furthermore, for the empirical study, they imply that researchers had better not choose WLS to estimate CFA model when the sample sizes are fewer than 200.
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