Two designs for comparing a judge's ratings with a known standard are compared: (1) Subjects are categorized into classes, with no knowledge of the size of either group; and (2) the judge is told the actual number allowed in each class. The probability distribution of the total number of correct choices is developed for each case, and their power…

Classical test theory findings can be derived from the concepts of conditional expectation, conditional independence, and related notions. It is shown that these concepts provide precisely the formalism needed to obtain the classical results with minimal assumptions and with greatest economy in the methods of proof. (RC)

Ordinal measurement is the rank ordering of individuals in a population. For ordinal measurement, the concept of an individual propensity distribution is his or her true score. Estimation of, as well as other aspects of the distribution, are discussed. (Author/JKS)

A Bayesian Model II approach to the estimation of proportions in m groups is extended to obtain posterior marginal distributions for the proportions. The approach is extended to allow greater use of prior information than previously and the specification of this prior information is discussed. (Author/RC)

Several Bayesian approaches to the simultaneous estimation of the means of k binomial populations are discussed. This has particular applicability to criterion-referenced or mastery testing. (Author/JKS)

An alternative to the uniform probability distribution model for ordinal data is considered. Implications for statistics and for test theory are discussed. (JKS)

Intraclass correlation and Cronbach's alpha are widely used to describe reliability of tests and measurements. Even with Gaussian data, exact distributions are known only for compound symmetric covariance (equal variances and equal correlations). Recently, large sample Gaussian approximations were derived for the distribution functions. New exact…