## Nominally Scored Items

In previous chapters, the examinee's free response to an item was scored on either a right-wrong or a graded basis. The repertoire of scoring procedures will now be extended to include nominal scoring of the responses to an item. Under nominal scoring, the possible responses to an item are allocated to m mutually exclusive, exhaustive, and nonordered categories. Thus, an examinee's free response to an item can be designated according to the category in which it belongs, but the category is represented by a nominal measure. For example, an item may consist of a complex mathematics problem to be solved and the examinee's solution scored as (A) heuristic, (B) algorithmic, (C) eclectic, or (D) trial and error, and no intrinsic ordering of these categories is assumed. As was the case with previous scoring procedures, the idea of scoring the free responses of an examinee does not match actual practice. Thus, an item will be considered to have m response categories, and the examinee is free to choose anyone of them. In the nominal response case, the examinee does not accumulate a total score since nominal measures cannot be summed. However, as shall be shown later, it is possible to estimate an examinee's ability using nominally scored items, even though a total score cannot be obtained. The item parameter estimation procedures associated with the nominal response case provide the solution to a problem that has long vexed educational measurement specialists, namely, how to estimate simultaneously the parameters of all the response alternatives to a multiple choice item. Thus, although items that are actually scored on a nominal basis are rare, this latter application has immediate and potentially widespread utility.