On maximizing item information and matching difficulty with ability

An important assumption in IRT model-based adaptive testing is that matching difficulty levels of test items with an examinee's ability makes a test more efficient. According to Lord, "An examinee is measured most effectively when the test items are neither too difficult nor too easy for him". This assumption is examined and challenged through a class of one-parameter IRT models including those of Rasch and the normal ogive. It is found that for a specific model, the validity of the fundamental assumption is closely related to the so-called van Zwet tail ordering of symmetric distributions. In this connection, the cosine distribution serves as the borderline between those satisfying the assumption and those violating the assumption. Graphic and numerical illustrations are presented to demonstrate the theoretic results.