Controlling Bias in Both Constructed Response and Multiple-Choice Items When Analyzed With the Dichotomous Rasch Model

Even though guessing biases difficulty estimates as a function of item difficulty in the dichotomous Rasch model, assessment programs with tests which include multiple-choice items often construct scales using this model. Research has shown that when all items are multiple-choice, this bias can largely be eliminated. However, many assessments have a combination of multiple-choice and constructed response items. Using vertically scaled numeracy assessments from a large-scale assessment program, this article shows that eliminating the bias on estimates of the multiple-choice items also impacts on the difficulty estimates of the constructed response items. This implies that the original estimates of the constructed response items were biased by the guessing on the multiple-choice items. This bias has implications for both defining difficulties in item banks for use in adaptive testing composed of both multiple-choice and constructed response items, and for the construction of proficiency scales.