A necessary and sufficient condition for a perfectly homogeneous test in the sense of Loevinger is stated and proved. Using this result, a formula for computing the maximum possible KR-20 when the test variance is assumed fixed is presented. A new index of test homogeneity is also presented and discussed. (Author/BW)

Four recent indices emphasizing the interrelationships of score distribution shape, modality, mean, and variance were investigated to determine the reliability of mastery tests. Attention was focused on the values of the indices when the cutoff score was near to or far from the modes of distribution. Five types of score distributions were…

An upper-asymptote parameter was added to the three-parameter logistic item response model. This four-parameter model was compared to the three-parameter model on four data sets. The fourth parameter increased the likelihood in only two of the four sets. Ability estimates for the students were generally unchanged by the introduction of the fourth…

Reliability coefficients of linear combinations of observed scores have anomalous properties which have led to difficulties in the investigation of difference scores and gain scores in test theory. Discrepancies between classical results and correct results obtained from more general formulas, which allow for correlated errors, are examined…

The binomial error model includes form-to-form difficulty differences as error variance and leads to Ruder-Richardson formula 21 as an estimate of reliability. If the form-to-form component is removed from the estimate of error variance, the binomial model leads to KR 20 as the reliability estimate. (Author/BW)

The Feldt-Gilmer congeneric reliability coefficients make it possible to estimate the reliability of a test composed of parts of unequal, unknown length. The approximate standard errors of the Feldt-Gilmer coefficients are derived via a method using the multivariate Taylor's expansion. Monte Carlo simulation is employed to corroborate the…

This paper considers, from a theoretical point of view, two measurement approaches used in measuring success and failure in skills tests in physical education. The first, "fixed length" (FL) testing, entails counting the number of successful performances in a fixed number of trials. The second, "trials-to-criterion" (TTC)…