Sample Size

Structural equation modeling (SEM) is an increasingly popular choice for quantitative statistical analyses, as it allows researchers to model complex relationships while taking into account measurement error of latent variables. Although there are great advantages to using SEM, the complexity of the analysis can be daunting, especially for students or beginning researchers. One of the most troublesome issues students face when using SEM is determining an appropriate sample size. For simple analyses like *t*-tests, ANOVAs, or regressions, reputable power analysis tools such as G*Power allow researchers to calculate an appropriate sample size using only a few basic parameters (i.e., power level, significance level, and effect size). For SEM, however, determining sample size is not as straightforward.

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Most researchers agree that SEM requires “large” sample sizes, but what exactly does this mean? A number that gets tossed around a lot is 300 (see Comrey & Lee, 2013; Tabachnick & Fidell, 2013), but a one-size-fits-all answer like this probably will not fly with most reviewers. As there is no single correct or universally-accepted calculation or method for determining sample size for SEM, researchers and students alike often rely on “rules of thumb.” For instance, some statistics scholars have recommended using the ratio of observations to estimated parameters (*N*:*q*) as a guide. Specifically, Kline (2015) recommended that the *N:q* ratio should be 20 to 1, or 20 observations (participants) for each estimated parameter in the model. Others have suggested that the *N:q* ratio can be as low as 10 to 1 (Schreiber et al., 2006) or 5 to 1 (Bentler & Chou, 1987). Clearly, there is a lot of variance and uncertainty even in guidelines proposed by SEM scholars.

So, what if your reviewers require some kind of hard calculation (rather than rules of thumb) to determine your sample size? Th

ere are some easy-to-use online tools that have academic support (for an example see Daniel Soper’s sample size calculation tool based on the work of Westland, 2010). However, Monte Carlo simulation is becoming an increasingly preferred method (for an in-depth discussion, see Wolf et al., 2013). In short, the Monte Carlo simulation method allows you to construct a model to your exact specifications and then test the model on thousands of “random” datasets of varying sample sizes. This lets you see approximately how often the effects in your model will be significant (i.e., statistical power) in a sample of any given size. The main advantage of this method is that it allows you to determine an appropriate sample size for the specific model you are testing. However, this method requires a high level of expertise in specific statistical software (such as Mplus) to conduct properly. Keep an eye out for future blogs where we may cover Monte Carlo methods in more detail!

**References**

Bentler, P. M., & Chou, C. P. (1987). Practical issues in structural modeling. *Sociological Methods & Research, 16*(1), 78-117.

Comrey, A. L., & Lee, H. B. (2013). *A first course in factor analysis*. Psychology Press.

Kline, R. B. (2015). *Principles and practice of structural equation modeling*. Guilford publications.

Schreiber, J. B., Nora, A., Stage, F. K., Barlow, E. A., & King, J. (2006). Reporting structural equation modeling and confirmatory factor analysis results: A review. *The Journal of Educational Research, 99*(6), 323-338.

Soper, D.S. (2018). A-priori Sample Size Calculator for Structural Equation Models . Available from http://www.danielsoper.com/statcalc

Tabachnick, B. & Fidell, L. (2013). *Using multivariate statistics.* Boston: Pearson Education.

Westland, J.C. (2010). Lower bounds on sample size in structural equation modeling. *Electronic Commerce Research and Applications, 9*(6), 476-487.

Wolf, E. J., Harrington, K. M., Clark, S. L., & Miller, M. W. (2013). Sample size requirements for structural equation models: An evaluation of power, bias, and solution propriety. *Educational and Psychological Measurement*, *73*(6), 913-934.