AN EMPIRICAL COMPARISON OF SELECTED ALTERNATIVES TO THE KUDER AND RICHARDSON FORMULA 20 (RELIABILITY, HOMOGENEITY, SIMULATION).

Abstract

Several alternatives to the Kuder and Richardson formula number 20 (KR20) were compared for accuracy using simulated and actual data sets. Coefficients by Loevinger (1948), Horst (1954), Raju (1982), and Cliff (1984) as well as the Kuder and Richardson formulae numbers 8 and 14 were examined. These alternative reliability coefficients were compared by (1) simulation of tests with varying degrees of item difficulty dispersion, subject proficiency, reliability, and length, and (2) use of the norming samples of the Curriculum Referenced Tests of Mastery (Charles E. Merrill Publishing Co., publisher) for grades four, six, and eight. Most of the coefficients examined proved no more accurate than the KR20 and several were decidedly worse. All coefficients, with the exception of Loevinger's, were affected by item difficulty dispersion. Two coefficients, the KR8 and Horst, were found to have potential as KR20 substitutes. These two coefficients are discussed with recommendations made as to the appropriate use of each one.