ERIC Number: ED250399
Record Type: RIE
Publication Date: 1984-Jun
Reference Count: 0
Multidimensional Difficulty as a Direction and a Distance.
Reckase, Mark D.; McKinley, Robert L.
The purpose of this paper is to present a generalization of the concept of item difficulty to test items that measure more than one dimension. Three common definitions of item difficulty were considered: the proportion of correct responses for a group of individuals; the probability of a correct response to an item for a specific person; and the location of the item along a difficulty continuum. This paper defines the difficulty of an item that measures more than one dimension as the direction from the origin of the multidimensional space to the point of greatest discriminating power and the distance from the origin to that point. The direction can be given in terms of angles with the coordinate axes or the corresponding direction cosines. The distance is a signed number using the same units as the coordinate axes. For the unidimensional case, the definition simplifies to the b-parameter from unidimensional item response theory. (BW)
Publication Type: Speeches/Meeting Papers; Reports - Research
Education Level: N/A
Sponsor: Office of Naval Research, Arlington, VA. Personnel and Training Research Programs Office.
Authoring Institution: N/A
Note: Paper presented at the Annual Meeting of the Psychometric Society (Santa Barbara, CA, June 1984).