A two-stage testing procedure, a routing test followed by one of several alternative second-stage tests, is studied in the situation where the purpose is measurement, not classification. Models are developed, examined, and compared with conventional tests and up-and-down procedures. (DG)

An upper-asymptote parameter was added to the three-parameter logistic item response model. This four-parameter model was compared to the three-parameter model on four data sets. The fourth parameter increased the likelihood in only two of the four sets. Ability estimates for the students were generally unchanged by the introduction of the fourth…

The stepped-up reliability coefficient does not have the same standard error as an ordinary correlation coefficient. Fisher's Z -transformation should not be applied to it. Appropriate procedures are suggested. (Author)