Sample size for confidence intervals for percentiles and application to cut-point determination

Percentiles are important parameters used in statistical applications. Many methods have been proposed for estimating confidence intervals for percentiles. In order to obtain a precise confidence interval, one needs to calculate the required sample size. One common measure of tightness for an interval is its width. Another measure of tightness for a tolerance-interval estimate is the proportion of the population covered by the interval at a specified confidence level. Hence, we propose a sample size determination approach based on the probability of over-coverage of the targeted percentile. In this paper, we derive sample size formulas for two confidence interval methods for percentiles under a normal distribution. For nonparametric methods for percentile estimation in unknown continuous distributions, we propose to determine the sample size based on an approximation method. An application to bioassay cut-point estimation is used to demonstrate the sample size determination.