n_effective: Effective sample size from cluster-robust standard errors

In alphaN: Set Alpha Based on Sample Size Using Bayes Factors

Effective sample size from cluster-robust standard errors

Description

Computes the effective sample size recommended by Wulff and Taylor (2024) for calibrating alpha with clustered (panel) data, where observations are not independent and the nominal sample size overstates the information in the data: n_e = n * (se / se_robust)^2, the total number of observations deflated by the squared ratio of the classical to the cluster-robust standard error. Vectorized over its arguments (recycled).

Usage

n_effective(n, se, se_robust)

Arguments

n	Total number of observations. A positive numeric vector.
se	The classical (non-robust) standard error of the coefficient.
se_robust	The cluster-robust standard error of the same coefficient.

Details

Wulff and Taylor (2024) recommend calibrating alpha with the total number of observations, which is the conservative choice, and then checking whether conclusions survive when alpha and the Bayes factor are recomputed with the effective sample size. Because cluster-robust standard errors typically exceed classical ones, n_effective() is typically smaller than n, which yields a larger calibrated alpha.

Value

A numeric vector with the effective sample size.

References

Wulff, J. N., & Taylor, L. (2024). How and why alpha should depend on sample size: A Bayesian-frequentist compromise for significance testing. Strategic Organization, 22(3), 550-581. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1177/14761270231214429")}

See Also

alphaN()

Examples

# A regression on 237 clustered observations where the cluster-robust
# standard error is twice the classical one implies an effective sample
# size four times smaller (Wulff & Taylor, 2024, Example 3)
n_effective(n = 237, se = 0.1, se_robust = 0.2)

# Alpha for moderate evidence at the nominal and the effective sample size
alphaN(n = 237, BF = 3, method = "robust")
alphaN(n = n_effective(237, 0.1, 0.2), BF = 3, method = "robust")

alphaN documentation built on July 27, 2026, 5:08 p.m.