Confidence Intervals for One Mean in a Stratified Design

This technical report outlines the procedure for calculating sample size and half-width for confidence intervals of a mean derived from a stratified design when the outcome variable is continuous. It discusses the importance of stratifying a population into subpopulations, or strata, to enhance estimation efficiency based on covariates such as age, race, or gender. The report provides detailed formulas for estimating the population mean and sample means within each stratum, as well as the expected value and variance of the sample mean. Additionally, it presents methods for sample size estimation, including equal, proportional, and optimum allocation strategies. An example illustrates the application of proportional allocation to determine sample size for a study aimed at estimating drug effectiveness across different age groups. The report concludes with numeric results and a strata-detail report summarizing the population sizes, sample sizes, and standard deviations for each stratum involved in the study.