Selecting Stopping Rules for Confidence Interval Procedures

The sample size decision is crucial to the success of any sampling experiment. More samples imply better confidence and precision in the results, but require higher costs in terms of time, computing power, and money. Analysts often choose sequential stopping rules on an ad hoc basis to obtain confidence intervals with desired properties without requiring large sample sizes. However, the choice of stopping rule can affect the quality of the interval produced in terms of the coverage, precision, and replication cost. This article introduces methods for choosing and evaluating stopping rules for confidence interval procedures. We develop a general framework for assessing the quality of a broad class of stopping rules applied to independent and identically distributed data. We introduce coverage profiles that plot the coverage according to the stopping time and reveal situations when the coverage could be unexpectedly low. Finally, we recommend simple techniques for obtaining acceptable or optimal rules.