BAYESIAN REGRESSION BETWEEN TRUE SCORES FOR PRETEST AND POSTTEST ANALYSIS

Abstract

The problem under consideration is to fit a straight line between true scores where, given n pairs of observed test scores, each observed score is assumed to be the sum of a true score and an error score. This problem may typically occur in the situation of pretest and posttest analysis. In order to facilitate the analysis, the split-halves technique is employed. Linearity between the split true scores is assumed as well as linearity between the true scores of the two tests. Based on these and other familiar assumptions, Bayesian estimates of the parameters, true scores, and reliability coefficients are derived.