# Source: Gau Research (2026) — original code demo, MIT License.
# Synthetic example only. Not a substitute for construct validity assessment.
set.seed(42)
n <- 120
latent <- rnorm(n)
x <- data.frame(
  item1 = latent + rnorm(n,sd=.5),
  item2 = latent + rnorm(n,sd=.6),
  item3 = latent + rnorm(n,sd=.7)
)
# Cronbach's alpha, manually using sample variance.
k <- ncol(x)
alpha <- (k / (k - 1)) * (1 - sum(sapply(x,var)) / var(rowSums(x)))
cat(sprintf('Demo Cronbach alpha = %.3f\n',alpha))