| Within the area of educational and cognitive research, there is an increasing emphasis on the structural organization of knowledge. This study is designed to contribute to the validity of the use Multidimensional Scaling (MDS) and Pathfinder analyses in assessing structural knowledge pertaining to the domain of introductory statistics. Eighty-nine beginning statistics students were asked to rate the relatedness of all pairwise combinations of 16 concepts that are commonly taught in beginning statistics courses (a total of 120 pairs). In addition, 11 experts in the field of statistics from several disciplines including Educational Psychology, Biometry, Mathematics and Statistics, and Sociology were asked to complete the same task. Multidimensional scaling and Pathfinder analyses were conducted on the relatedness ratings in order to identify the cognitive structure of statistics knowledge. Quantitative indexes of similarity of structures between students and experts were computed, including the Pathfinder C Coefficient of similarity, correlations of the Graph Theoretic Distances between concepts, correlations of the Euclidean Distances between concepts, Angular Distances between weighted MDS vectors, and correlations of the raw relatedness ratings.; Results indicated that both MDS and Pathfinder yielded useful visual depictions of knowledge organization. However, there is little evidence to support the predictive validity of these techniques. Similarity to one's statistics instructor or to any other single expert or expert group failed to uniformly predict statistics achievement. In addition, a comparison of expert knowledge structures indicates that the domain of introductory statistics may not have an inherent, consistent structure. |
