How to Calculate Sample Size in Structural Equation Modelling (SEM) - Inverse Square Root Method

Structural equation modelling in PLS (PLS-SEM/PLS SCM) can produce solutions with smaller samples, but sample size still has to match the population and the analysis requirements. A common misconception—that “any small sample will still be accurate”—fails once researchers consider how heterogeneous the target population is and how multivariate techniques depend on adequate statistical power. When sample size falls short, real effects can remain undetected, creating a Type II error; even worse, results may not generalize, so a model estimated on one sample can yield different conclusions than the same model estimated on a larger sample from the same population.

The transcript highlights that minimum sample size guidelines matter because they help ensure robustness and generalizability for methods such as PLS-SEM. It also criticizes the widely cited “10-times rule,” which recommends setting sample size to ten times the number of independent variables in the most complex regression (including both measurement and structural parts). That shortcut can mislead researchers because it ties sample size to model complexity in a way that ignores other determinants—especially the expected effect size and the statistical testing conditions.

To address these issues, Co and Hada (2018) propose the inverse square root method for calculating minimum sample size. The method focuses on the probability that the ratio of a path coefficient to its standard error exceeds the critical value of the test statistic at a chosen significance level. In practice, the minimum sample size depends on the path coefficient (the strength of the hypothesized effect) and the selected significance level—not on the size of the most complex formative model or the overall model size, and not on a single parameter alone.

The transcript describes how to compute n_min using separate equations for common significance levels: 1%, 5%, and 10%. It then walks through an example at a 5% significance level: with a minimum path coefficient of 0.20, the minimum sample size comes out to about 154.2, which is rounded up to the next integer (155). The method is described as conservative because it tends to slightly overestimate the sample size needed to achieve the desired power (assumed at 80%) for detecting an effect.

Because researchers often lack precise expectations for effect sizes—even when a pilot study exists—the transcript recommends using ranges of plausible path coefficients rather than a single value. It suggests taking the upper boundary of the effect-size range when applying the inverse square root method, again reflecting the method’s conservative nature. For instance, if the expected minimum path coefficient is somewhere between 0.11 and 0.20 at a 5% significance level, the calculation uses the upper value (0.20), leading to roughly 155 observations. Similar lookups are provided for other effect ranges (e.g., 0.21–0.30 and 0.31–0.40), producing corresponding minimum sample sizes.

Overall, the core takeaway is that defensible sample size planning in PLS-SEM should be tied to statistical power, significance level, and the expected magnitude of the path effect—rather than relying on simplified rules that ignore these drivers of Type II error and generalizability.