An Item Response Model for True–False Exams Based on Signal Detection Theory

Abstract

A true–false exam can be viewed as being a signal detection task—the task is to detect whether or not an item is true (signal) or false (noise). In terms of signal detection theory (SDT), examinees can be viewed as performing the task by comparing the perceived plausibility of an item (a perceptual component) to a threshold that delineates true from false (a decision component). The resulting model is distinct yet is related to item response theory (IRT) models and grade of membership models, with the difference that SDT explicitly recognizes the role of examinees’ perceptions in determining their response to an item. SDT also views IRT concepts such as “difficulty” and “guessing” in a different light, in that both are viewed as reflecting the same aspect—item bias. An application to a true–false algebra exam is presented and the various models are compared.