A General Approach to Algorithmic Design of Fixed-Form Tests, Adaptive Tests, and Testlets

Abstract

The selection of items from a calibrated item bank for fixed-form tests is an optimal test design problem; this problem has been handled in the literature by mathematical programming models. A similar problem, however, arises when items are selected for an adaptive test or for testlets. This paper focuses on the similarities of optimal design of fixed-form tests, adaptive tests, and testlets within the framework of the general theory of optimal designs. A sequential design procedure is proposed that uses these similarities. This procedure not only enables optimal design of fixed-form tests, adaptive tests, and testlets, but is also very flexible. The procedure is easy to apply, and consistent estimates for the trait level distribution are obtained. Index terms: adaptive tests, consistency, efficiency, optimal test design, sequential procedure, test design, testlets.