Power analysis is a fundamental prerequisite for conducting scientific research. Without power analysis the researcher has no way of knowing whether the sample size is large enough to detect the effect he or she is looking for. This paper demonstrates how psychometric factors such as measurement error and equating error affect the power of…

To resolve a recent controversy between Klein and Cleary and Levy, a model for dichotomous congeneric items is presented which has mean errors of zero, dichotomous true scores that are uncorrelated with errors, and errors that are mutually uncorrelated. (Author)

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)

The problem of whether a precise connection exists between the stochastic processes considered in mathematical learning theory and the Guttman simplex is investigated. The approach used is to derive a set of conditions which a probabilistic model must satisfy in order to generate inter-trial correlations with the perfect simplex property.…

Using the concepts of conditional probability, conditional expectation, and conditional independence, the main results of the classical test theory model can be derived in a very few steps with minimal assumptions. The present effort explores the possibility that present classical test theories can be further condensed. (Author/RC)

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