Measuring and Comparing Student Performance:A New Technique for Assessing Directional Associations

Abstract: Measuring and comparing student performance have been topics of much interest for educators and psychologists. Particular attention has traditionally been paid to the design of experimental studies and careful analyses of observational data. Classical statistical techniques, such as fitting regression lines, have traditionally been utilized and far-reaching policy guidelines offered. In the present paper, we argue in favour of a novel technique, which is mathematical in nature, and whose main idea relies on measuring distance of the actual bivariate data from the class of all monotonic (increasing in the context of this paper) patterns. The technique sharply contrasts the classical approach of fitting least-squares regression lines to actual data, which usually follow non-linear and even non-monotonic patterns, and then assessing and comparing their slopes based on the Pearson correlation coefficient, whose use is justifiable only when patterns are (approximately) linear. We describe the herein suggested distance-based technique in detail, show its benefits, and provide a step-by-step implementation guide. Detailed graphical and numerical illustrations elucidate our theoretical considerations throughout the paper. The index of increase, upon which the technique is based, can also be used as a summary index for the LOESS and other fitted regression curves.