Review of Sample Size for Structural Equation Models in Second Language Testing and Learning Research: A Monte Carlo Approach

The importance of sample size, although widely discussed in the literature on structural equation modeling (SEM), has not been widely recognized among applied SEM researchers. To narrow this gap, we focus on second language testing and learning studies and examine the following: (a) Is the sample size sufficient in terms of precision and power of parameters in a model using Monte Carlo analysis? (b) How are the results from Monte Carlo sample size analysis comparable with those from the N >= 100 rule and from the N: q >= 10 (sample size-free parameter ratio) rule? Regarding (a), parameter bias, standard error bias, coverage, and power were overall satisfactory, suggesting that sample size for SEM models in second language testing and learning studies is generally appropriate. Regarding (b), both rules were often inconsistent with the Monte Carlo analysis, suggesting that they do not serve as guidelines for sample size. We encourage applied SEM researchers to perform Monte Carlo analyses to estimate the requisite sample size of a model.