Publications & Resources

Multidimensional Description of Subgroup Differences in Mathematics Achievement Data From the 1992 National Assessment of Educational Progress

Jun 1997

Bengt O. Muthén, Siek-Toon Khoo, and Ginger Nelson Goff

This report investigates the dimensionality of the 1992 NAEP mathematics test in the context of subgroup differences. A multidimensional model is supported by these data with dimensions corresponding to both content-specific and format-specific factors. The analysis approach of this paper utilizes key grouping variables of the NAEP reports (e.g., gender, ethnicity) but has the advantage that subgroup comparisons are done not only in a univariate manner, using one grouping variable at a time, but using the set of grouping variables jointly. This is carried out within a structural model with latent variables, which relates the information on the test items to background information via a set of factors. It is found that the different factors relate differently to the background variables. Multidimensional latent variable modeling also suggests a new way of reporting results with respect to math performance in specific content areas. For content-specific performance, the subscores are related to overall performance, considering content-specific scores conditional on overall scores. For a given overall score, a subgroup difference is considered with respect to a certain content area. This conditional approach may be of value for revealing differences in opportunity to learn or differences in curricular emphases. Conditional differences may be viewed as “unrealized potential” for performance in a specific content area.

Muthén, B. O., Khoo, S.- T., & Goff, G. N. (1997). Multidimensional description of subgroup differences in mathematics achievement data from the 1992 National Assessment of Educational Progress (CSE Report 432). Los Angeles: University of California, Los Angeles, National Center for Research on Evaluation, Standards, and Student Testing (CRESST).