The pure Rasch model was compared with four modifications of the model in a number of different simulations in order to ascertain the comparative efficiencies of the parameter estimations of these modifications. Because there is always noise in test score data, some individuals may have response patterns that do not fit the model and their…

A mathematics item on the Scholastic Aptitude Test (SAT) was found to be faulty and received wide publicity. A detailed investigation into its mathematical and psychometric properties is presented. It was found that the problem could be considered ambiguous but that almost no one noticed the ambiguity. (Author/JKS)

It is important to estimate the number of examinees who reached a test item, because item difficulty is defined by the number who answered correctly divided by the number who reached the item. A new method is presented and compared to the previously used definition of three categories of response to an item: (1) answered; (2) omitted--a…