Distractors with information in multiple choice items: a rationale based on the Rasch model

There is a substantial literature on attempts to obtain information on the proficiency of respondents from distractors in multiple choice items. Information in a distractor implies that a person who chooses that distractor has greater proficiency than if the person chose another distractor with no information. A further implication is that the distractor deserves partial credit. However, it immediately follows from the Rasch model that if a distractor deserves partial credit, then the response to that distractor and other distractors should not be pooled into a single response with a single probability of an incorrect response. Using the partial credit parameterization of the polytomous Rasch model, the paper shows how an hypothesis can be formed, and tested, regarding information in a distractor. The hypothesis is formed by studying the shape of the distractor response curves across the continuum, and the hypothesis is tested by scoring the correct response 2, the hypothesized distractor 1, and other distractors 0, and then applying the polytomous Rasch model. Multiple pieces of evidence, including fit of the responses at the two thresholds and the order of the two threshold estimates, are used in deciding if a distractor has information. An example illustrating the theory and its application is provided.