Variances and Asymptotic Distributions of Direct Standardized Rates

Formulas for the variance of direct standardized rates are given for three different sampling models. The three models are product multinomial models when population totals are fixed by design, or strata totals are fixed by design, or cell (each population—each stratum) totals are fixed by design. Asymptotic distributions are derived for each model. A discussion on the relevance and use of standardized rates and the need for distribution theory is also provided.