Comparison of Seriation and Multidimensional Scaling: Two Techniques for Validating Constructs in Physical Education
Diane M. Korell, Margaret J. Safrit · Research Quarterly for Exercise and Sport · 1977
Several scaling techniques were identified as procedures that might be useful in the statistical validation of constructs in physical education. The purpose of this study was to examine solutions obtained by the techniques of seriation and multidimensional scaling, one- and two-dimensional, as varying degrees of error were introduced into specific data sets. Using a Monte Carlo model, four different sized matrices were selected to represent situations that could be applicable to research problems in physical education, such as ordering developmental sequences, course objectives, and levels of behavior in curriculum hierarchies. Kendall's tau (τ) values were computed between the ordering resulting from the matrix with no error and all other solutions for a particular matrix size in order to compare the solutions utilizing various scaling techniques, matrix sizes, and degrees of error. An analysis of variance of the 4 × 3 × 3 design of the study yielded three significant main effects of matrix size, random error, and scaling technique. Tau values served as the dependent measures with ten replications per cell. The following results were obtained: (a) the larger matrix sizes produced the most accurate results; (b) as error increased, the accuracy of all solutions decreased; (c) the technique of seriation produced slightly more accurate solutions than one- and two-dimensional multidimensional scaling.