Dimensionality of 1990 NAEP Mathematics Data / James E. Carlson and Tom Jirele.

Some results are presented relating to the dimensionality of the 1990 National Assessment of Educational Progress (NAEP) mathematics item-response data. Based on theoretical considerations, practical limitations, and previous research, two procedures were selected for study: full information factor analysis as implemented in the TESTFACT computer program and normal harmonic factor analysis as implemented in the NOHARM computer program. One-dimensional, two-dimensional, and three-dimensional models were fitted using both programs. NOHARM analysis used 941 fourth-grade examinees with 50 items, 914 fourth-grade examinees with 42 items, 917 eighth-grade examinees with 54 items, and 924 eighth-grade examinees with 58 items. Sixteen TESTFACT analyses were conducted with real data sets. Comparisons show better fit when data are known to be one dimensional than in the case of real NAEP data. The results seem consistent over both programs and over different data sets. There is, however, evidence of a strong first dimension fitting the examinee-item interaction data. Overall, it is suggested that data are sufficiently unidimensional to support use of a composite scale for describing NAEP data, although there is evidence that two dimensions would better fit the data than would one dimension. Eight tables and 23 graphs present analysis results, and there is a 33-item list of references. (SLD)

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