A critical issue of using the variance of the total in the linearization method - In the context of unequal probability sampling.

Publicly available national survey data are useful for the evidence-based research to advance our understanding of important questions in the health and biomedical sciences. Appropriate variance estimation is a crucial step to evaluate the strength of evidence in the data analysis. In survey data analysis, the conventional linearization method for estimating the variance of a statistic of interest uses the variance estimator of the total based on linearized variables. We warn that this common practice may result in undesirable consequences such as susceptibility to data shift and severely inflated variance estimates, when unequal weights are incorporated into variance estimation. We propose to use the variance estimator of the mean (mean-approach) instead of the variance estimator of the total (total-approach). We show a superiority of the mean-approach through analytical investigations. A real data example (the National Comorbidity Survey Replication) and simulation-based studies strongly support our conclusion.