A Logistic Model for Time-Limit Tests

Abstract

The purpose of the present chapter is to introduce a psychometric model for time-limit tests. Our point of departure is a practical one. The main problem involved in the use of time-limit tests may be illustrated by the following example. Assume that a test consists of a large number of equally difficult items, and that examinees are allowed to answer the items during a fixed amount of time τ. Suppose person A and person B both have the same proportion of correct answers, but have completed a different number of items. Should the ability estimates of A and B be equal? It may be argued that for several reasons the answer should be no. The most practical reason may be that if only the proportion correct is important, the optimal strategy in answering the test is to spend all the allotted time on the first item. But also in realistic settings, where examinees are urged to work fast but accurately, a response style which favors accuracy at the expense of speed is advantageous. It might seem that using the number of correct responses reflects both speed and accuracy, and is therefore a more sensible way of scoring the test performance. But with this approach, another problem crops up. If the test consists of n items, the number of correct responses can be expressed as a proportion relative to n, implying that items not reached and wrong responses are treated in the same way, an approach which may prejudice to persons working slowly but accurately.