Item Response Theory

 Resources

Item Response Theory is the study of test and item scores based on assumptions concerning the mathematical relationship between abilities (or other hypothesized traits) and item responses. Other names and subsets include Item Characteristic Curve Theory, Latent Trait Theory, Rasch Model, 2PL Model, 3PL model and the Birnbaum model.

In the following figure, the x-axis represents student ability and the y-axis represents the probability of a correct response to one test item. The s-shaped curve, then, shows the probabilities of a correct response for students with different ability (theta) levels.

Modeling  the relationships between ability and a set of items provides the basis for numerous practical applications, most of which have advantages over their classical measurement theory counterparts. 

The goal of this page is to provide resources to help you learn more about this class of measurement models. The main feature of this page is Frank Baker's exceptional book, The Basics of Item Response Theory, which we have made available, in its entirely, on-line, at no cost. This delightful book will allow you to acquire the basic concepts of the theory without becoming enmeshed in the underlying mathematics and computational complexities. We hope you will take advantage of this important contribution by Dr. Baker.

December 2001
Lawrence M. Rudner