Several extended caution indices (ECIs) have been introduced earlier as a link between two distinctly different approaches: one based on standard statistics and the other, a model-based approach, utilizing item response theory (IRT). Expected values and variance of some ECIs are derived and their statistical properties are compared and discussed.…

The progress of modern mental test theory depends very much on the techniques of maximum likelihood estimation, and many popular applications make use of likelihoods induced by logistic item response models. While, in reality, item responses are nonreplicate within a single examinee and the logistic models are only ideal, practitioners make…

This paper describes the development of a language arts test to assess the consistency of student response patterns and the feasibility of using the test to diagnose students' misconceptions. The studies were part of a project to develop computerized adaptive testing for the language arts with software to diagnose student errors. The…