ERIC Number: ED331845
Record Type: RIE
Publication Date: 1991-Apr
Reference Count: N/A
Interpretation of Number-Correct Scores when the True Number of Dimensions Assessed by a Test Is Greater than Two.
Reckase, Mark D.; Hirsch, Thomas M.
This paper addresses the problem of whether two-dimensional solutions with different apparent meanings and different implied interpretations of the number-correct scale could be produced from the same test data set by simply shifting the orientation of the two-dimensional projection plane. An artificial data set of 3,000 response vectors and a real data set (3,153 examinees) obtained from administration of the American College Testing Program 60-item Mathematics Test were used. For the artificial data set, the alternative orientations of the two-dimensional projection plane in the three-dimensional space did suggest different interpretations of the unidimensional score. The relative position of item vectors changed with each orientation, and the definition of the axes in the two-dimensional solution was different in each orientation. Results with the real data were not as clear as those for the artificial data; however, some differences in the dimensions of the solutions were apparent. Results imply that multidimensional exploratory analyses should follow a strategy that emphasizes determining the largest number of dimensions that yield meaningful results, rather than the smallest number of dimensions that come close to reproducing the relationships in the data. Five tables and five graphs illustrate the discussion. (SLD)
Publication Type: Reports - Research; Speeches/Meeting Papers
Education Level: N/A
Sponsor: Office of Naval Research, Arlington, VA. Cognitive and Neural Sciences Div.
Authoring Institution: N/A
Identifiers: ACT Mathematics Placement Examination; Exploratory Factor Analysis; Number Right Scoring; Unidimensionality (Tests)
Note: Paper presented at the Annual Meeting of the National Council on Measurement in Education (Chicago, IL, April 4, 1991).