Direct and Inverse Problems of Item Pool Design for Computerized Adaptive Testing

The recent literature on computerized adaptive testing ( CAT) has developed methods for creating CAT item pools from a large master pool. Each CAT pool is designed as a set of nonoverlapping forms reflecting the skill levels of an assumed population of test takers. This article presents a Monte Carlo method to obtain these CAT pools and discusses its advantages over existing methods. Also, a new problem is considered that finds a population ability density function best matching the master pool. An analysis of the solution to this new problem provides testing organizations with effective guidance for maintaining their master pools. Computer experiments with a pool of Law School Admission Test items and its assembly constraints are presented.