This paper discusses methods for evaluating the first-stage sample design of complex
sample designs. We need these methods because the Bureau of Labor Statistics is in the
process of redesigning the 2020 sample design of the Consumer Expenditures Surveys. The
research is important because we only have the opportunity to redesign the first stage every
ten years. The paper provides expressions for the variance of the collapsed strata estimator
and the with replacement variance estimator and uses those expressions to evaluate
alternative sample designs for the 2020 redesign of the Consumer Expenditures Surveys.