Estimating Item Difficulty

Abstract

To estimate the difference in difficulty between two dichotomous items the equation conditioning on the total scoreTotal scoreand eliminating the person parameter is applied. In the solution equation, the proportion of persons who have answered one item correctly and the other incorrectly is an estimate of the probability of answering that item correctly, given a total scoreTotal scoreof 1 on the two items. Only the difference in difficulty is estimated, i.e. the items’ relative difficulties. By setting an arbitrary originArbitrary originof 0, i.e. constraining the item locations to sum to 0, each item is given its own location value. Estimating item difficulties is called item calibrationItem calibration. However, the estimated difference in difficulties is expressed in an arbitrary unitArbitrary unit. The sense in which the unitUnitis arbitrary is explained. Although the origin and unitUnitare arbitrary in each analysis, they may be fixed for some convenient reason to a priori values. Statistics Review 10: Bernoulli and Binomial random variables.