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Structural Equation Model Sample Size Formulas

Below you will find descriptions and details for the 3 formulas that are used to compute sample sizes for structural equation model (SEM) studies involving latent variables.

Cumulative distribution function (CDF) for the normal distribution:
Cumulative distribution function (CDF) for the normal distribution formula
Variable definitions:
ยต = mean
σ = standard deviation
erf = error function
Error function:
Error function formula
Structural equation model (SEM) lower bound sample size:
Structural equation model (SEM) lower bound sample size formula
Variable definitions:
j = number of observed variables
k = number of latent variables
ρ = estimated Gini correlation for a bivariate normal random vector
δ = anticipated effect size
α = Sidak-corrected Type I error rate
β = Type II error rate
z = a standard normal score
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