Minimum Sample Size Rule for STSRS: A Three-Term Edgeworth Expansion for the Studentized Sample Mean

Thomas M. Menino Convention & Exhibition Center 

The purpose of this paper is to 1) develop a three-term Edgeworth expansion to the order n^(-1) for the Studentized sample mean under stratified simple random sampling from a finite population and 2) use this expansion to establish minimum sample size rules for STSRS that measure the normal approximation of the Studentized sample mean with a user-specified coverage tolerance for the traditional one- or two-sided confidence interval of the population mean. The new rules improve the extended Cochran's sample size rule previously established by Qing and Valliant (2025) from a two-term Edgeworth expansion of the same statistic, yielding less conservative sample size thresholds across common allocations. In simulations spanning a wide range of skewed finite populations, the performance of the new rules is evaluated.

Confidence interval

Coverage probability

Edgeworth expansion

Minimum sample size

Stratified simple random sampling 

Survey Research Methods Section