We first review existing literature on cumulative logit models along with various ways to test the parallel lines assumption. Building on the traditional frequentist framework, we introduce a method of Bayesian assessment of null values to provide an alternative way to examine the parallel lines assumption using highest density intervals and…

In 1881, Donald MacAlister posed a problem in the "Educational Times" that remains relevant today. The problem centers on the statistical evidence for the effectiveness of a treatment based on a comparison between two proportions. A brief historical sketch is followed by a discussion of two default Bayesian solutions, one based on a…

Cluster randomized experiments are ubiquitous in modern education research. Although a variety of modeling approaches are used to analyze these data, perhaps the most common methodology is a normal mixed effects model where some effects, such as the treatment effect, are regarded as fixed, and others, such as the effect of group random assignment…

Regression equations have many useful roles in psychological assessment. Moreover, there is a large reservoir of published data that could be used to build regression equations; these equations could then be employed to test a wide variety of hypotheses concerning the functioning of individual cases. This resource is currently underused because…

A latent variable analysis procedure for evaluation of reliability coefficients for 2-level models is outlined. The method provides point and interval estimates of group means' reliability, overall reliability of means, and conditional reliability. In addition, the approach can be used to test simple hypotheses about these parameters. The…

This article presents a didactic discussion on the role of asymptotically independent test statistics and separable hypotheses as they pertain to issues of specification error, power, and model misspecification in the covariance structure modeling framework. A small population study supports the major findings. (SLD)