Modern Sequential Analysis and its Applications to Computerized Adaptive Testing

TL;DR

This paper reviews recent advances in sequential analysis, especially generalized likelihood ratio tests, and applies them to design asymptotically optimal computerized adaptive mastery tests that outperform traditional methods.

Contribution

It extends asymptotic optimality theory to sequentially generated experiments and demonstrates their application in designing superior adaptive mastery tests.

Findings

Adaptive tests are asymptotically optimal.

Proposed methods outperform existing sequential and fixed-length tests.

Extensions to sequentially generated experiments are validated.

Abstract

After a brief review of recent advances in sequential analysis involving sequential generalized likelihood ratio tests, we discuss their use in psychometric testing and extend the asymptotic optimality theory of these sequential tests to the case of sequentially generated experiments, of particular interest in computerized adaptive testing. We then show how these methods can be used to design adaptive mastery tests, which are asymptotically optimal and are also shown to provide substantial improvements over currently used sequential and fixed length tests.