Sample size for SEM

Calculate how many people you need for a structural equation model. We explain every input in plain words, so you know what you are entering and why.

How do you want to enter your model?

Build my model (we guide you step by step) I know my numbers (type them in)

Step 1 · Build your model's structure

Add each variable in your study. If its scale has dimensions (subscales), add them with the number of items in each. We count the latent and observed variables for you.

Add your variables to see the summary.

Step 2 · Complete the remaining inputs

Number of latent variables

Filled in automatically from your Step 1 model.

Number of observed variables

Filled in automatically from your Step 1 model.

Expected effect size

The smallest relationship between two variables that you want to be able to detect.

Desired statistical power

Probability of finding the relationship if it really exists. 0.80 is typical.

Significance level (α)

The risk you accept of seeing a relationship that does not exist. 0.05 is typical.

Recommended minimum sample

—

To detect the effect: —
For the model structure: —

Plain-language guide

What do you need to know?

What is SEM?

A structural equation model (SEM) tests, all at once, how several things you want to measure relate to one another. For example, whether academic stress affects well-being through self-efficacy.

Latent variable

It is what you want to study but cannot see or measure directly: anxiety, satisfaction or leadership. That is why you measure it with a questionnaire. Every construct in your model is a latent variable.

Observed variable

It is each question or item that people do answer and that can be recorded. If your stress scale has 10 questions, that latent variable has 10 observed variables.

Dimensions

Some scales are split into parts that measure different aspects of the same variable. For example, anxiety can have a cognitive dimension and a somatic one. In the model, each dimension is its own latent variable, measured with its own items.

General factor

When you want the whole variable (for example, "Anxiety") to appear in the model above its dimensions, you add a general factor, also called a second-order factor. It counts as one more latent variable, even though it has no items of its own: it is measured through its dimensions. If your model only uses the dimensions separately, uncheck that box.

Effect size

It is the smallest relationship between two latent variables that you want to detect, expressed as a correlation: 0.1 is small, 0.3 medium and 0.5 large (Cohen, 1988). If you have no previous studies to guide you, 0.3 is a common starting point. The smaller the effect, the larger the sample you need.

Power and significance

Power (usually 0.80) is the probability of finding the relationship if it exists. Significance (usually 0.05) is the risk you accept of being wrong when you say there is a relationship.

Example

Your model has three variables. Anxiety has two dimensions (cognitive and somatic) with 5 items each, plus a general factor. Self-efficacy is measured with 8 items and well-being with 6, without dimensions.

Latent variables: 5 (2 + 1 + 1 + 1)
Observed variables: 24 (5 + 5 + 8 + 6)
Effect size: 0.3
Power: 0.80
Significance (α): 0.05

Result: 150 to detect the effect and 92 for the structure, so you need at least 150 participants.

How is it calculated?

We use Westland's (2010) procedure, the same one used by Soper's calculator, which combines two criteria and recommends the larger one:

To detect the effect: the minimum sample needed to distinguish, with the power and significance you chose, a relationship of the stated size between any pair of latent variables. Significance is adjusted with the Šidák correction because the model tests many relationships at once.
For the model structure: n = 50r² − 450r + 1100, where r is the number of observed variables per latent variable. It summarizes simulation studies showing that, with few items per variable, the model needs a larger sample.

These values are minimums. With data that are not normally distributed (for example, highly skewed Likert scales), with very complex models or with many incomplete responses, a larger sample is advisable. For very complex models, the most accurate method is Monte Carlo simulation.

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

How to cite this tool

AtheneaLab. (2026). Sample size for SEM [Web application]. https://athenealab.com/en/sample-size/sem/

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