Minimum Sample Sizes with Rare Events in Stratified Designs

There are many statistical issues in using stratified sampling for rare events. They include designing to ensure enough of the rare events are found in each stratum, achieving adequate accuracy of the estimates and their variance, and meeting the normality assumptions for confidence interval construction. When sampling to estimate sales and use tax, a large population is sampled to find a rare event (taxable amount) and a small ratio is calculated. Many state taxing authorities that use statistical sampling in sales and use tax studies require minimum stratum sample sizes of anywhere between 100 to 350 records. In this paper we study when this minimum requirement is too much, too little, or just right. Simulation was used to assess the adequacy of stratum sample sizes. We examined the accuracy of estimation, relative precision, frequency of under/over estimation, and calculation of confidence intervals. The results of the simulations show that in some situations samples could be reduced if more information about estimated values were known in advance. This information could be obtained through historical information or through a pilot study.