A Tutorial on Assessing Statistical Power and Determining Sample Size for Structural Equation Models

Translational Abstract Structural equation modeling (SEM) is a widespread approach to test substantive hypotheses in psychology and other social sciences. Whenever hypothesis tests are performed, researchers should ensure that the sample size is sufficiently large to detect the hypothesized effect. Power analyses can be used to determine the required sample size to identify the effect of interest with a desired level of statistical power (i.e., the probability to reject an incorrect null hypothesis). Vice versa, power analyses can also be used to determine the achieved power of a test, given an effect and a particular sample size. However, most studies involving SEM neither conduct a power analysis to inform sample size planning nor evaluate the achieved power of the performed tests. In this tutorial, we show and illustrate how power analyses can be used to identify the required sample size to detect a certain effect of interest or to determine the probability of a conducted test to detect a certain effect. These analyses are exemplified regarding the overall model as well as regarding individual model parameters, whereby both, models referring to a single group as well as models assessing differences between multiple groups are considered. Structural equation modeling (SEM) is a widespread approach to test substantive hypotheses in psychology and other social sciences. However, most studies involving structural equation models neither report statistical power analysis as a criterion for sample size planning nor evaluate the achieved power of the performed tests. In this tutorial, we provide a step-by-step illustration of how a priori, post hoc, and compromise power analyses can be conducted for a range of different SEM applications. Using illustrative examples and the R package semPower, we demonstrate power analyses for hypotheses regarding overall model fit, global model comparisons, particular individual model parameters, and differences in multigroup contexts (such as in tests of measurement invariance). We encourage researchers to yield reliable-and thus more replicable-results based on thoughtful sample size planning, especially if small or medium-sized effects are expected.

Automated summary

Structural equation modeling (SEM) is commonly used in psychology and other social sciences to test empirical hypotheses. However, most studies involving SEM do not conduct power analysis for sample size planning or evaluate the achieved power of the tests. This tutorial provides step-by-step instructions on a priori, post hoc, and compromise power analyses for various SEM applications. It emphasizes the importance of thoughtful sample size planning to ensure reliable and replicable results, particularly when small or medium-sized effects are expected.