The degrees of freedom of a variance estimator in a probability sample

Inferences from probability-sampling theory (more commonly called “design-based sampling theory”) often rely on the asymptotic normality of nearly unbiased estimators. When constructing a two-sided confidence interval for a mean, the ad hoc practice of determining the degrees of freedom of a probability-sampling variance estimator by subtracting the number of its variance strata from the number of variance primary sampling units (PSUs) can be justified by making usually untenable assumptions about the PSUs. We will investigate the effectiveness of this conventional and an alternative method for determining the effective degrees of freedom of a probability-sampling variance estimator under a stratified cluster sample.