Extending Cochran’s Sample Size Rule to Stratified Simple Random Sampling with Applications to Audit Sampling

Audit samples are selected by businesses, institutions, government agencies, and other organizations to check the accuracy of financial reports and assess the quality of services provided among other reasons. A standard design used in auditing is stratified simple random sampling. Point estimates and confidence intervals for population values are usual products of an audit. Cochran’s sample size rule and its extension by Sugden, Smith, and Jones provided minimum sample size formulas for a simple random sample to ensure effective normal approximation and adequate coverage for nominal 95% confidence intervals of a standardized or Studentized sample mean. The purpose of this paper is to extend Cochran’s rule and establish a formula for the minimum sample size for the normal approximation and the use of traditional one-sided or two-sided confidence intervals to be acceptable for mean estimation in stratified simple random samples. We concentrate on variables that are at least partially continuous. Simulations are used to examine the performance of our sample size formula with a variety of skewed populations based on ones encountered in auditing.