Discusses Melvin R. Novick's work in the area of Bayesian statistics. This area of statistics was seen as a powerful scientific tool that allows educational researchers to have a better understanding of their data. (RB)

The threshold utility model for culture-fair selection is defined for both quota-free and for restricted selection. In addition a full Bayesian solution based on posterior predictive distributions is provided. Mathematical derivations and an example are provided. (JKS)

A least squares statistical procedure for fitting utility functions is extended to truncated normal and extended beta functions. Implications for educational decision-making are discussed. (JKS)

A Bayesian solution is presented for the Johnson-Neyman problem (whether or not the distance between two regression lines is statistically significant over a finite interval of the independent variable). (Author/CTM)

A simple example is presented that illustrates advantages of Bayesian and likelihood methods of inference relative to sampling distribution methods of inference. It is argued that Bayesian and likelihood methods of inference should be utilized more generally to analyze real data. (Author/CTM)

When the experimental units are measured twice, and the response variable is dichotomous, the equality of the two proportions is usally assessed by Mc Nemar's (1947) test. In this paper, Bayesian methods are presented for testing hypotheses regarding the two success probabilities in light of complete and incomplete data. (Author/BW)

Fisher's two-group discriminant function has been generalized in two different ways for the case of three or more groups, leading to confusion in the literature. The precise functional relation between the two functions is derived, and the interpretation of the two functions is discussed. An example is provided. (Author/CTM)

Based on the Gaussian model, methods for using measurements that depend on the true attribute to compute rankings are proposed and compared. Measurements based on an empirical Bayes model produce estimates that differ from ranking observed data. Ranking methods are illustrated with school achievement data. (TJH)

In the case of dichotomous decisions, the total set of all assumptions/specifications for which the decision would have been the same is the robustness region. Inspection of this (data-dependent) region is a form of sensitivity analysis which may lead to improved decision making. (Author/BW)

Estimation theory in educational statistics and the application of hierarchical linear models are reviewed. Observations within each group vary as a function of microparameters. Microparameters vary across the population of groups as a function of macroparameters. Bayes and empirical Bayes viewpoints review examples with two levels of hierarchy.…

The use of Bayesian and empirical Bayesian techniques to summarize results from parallel randomized experiments is illustrated using the results of eight such experiments from an SAT coaching study. Graphical techniques, simulation techniques, and methods for monitoring the adequacy of model specification are highlighted. (Author/JKS)

Computation and interpretation of Bayesian full-rank multivariate analysis of variance and covariance is described and illustrated in an exposition intended for readers familiar with univariate analysis of variance and multiple regression. (Author)

An approach is presented to simultaneously optimize decision rules for combinations of elementary decisions through a framework derived from Bayesian decision theory. The developed linear utility model for selection-mastery decisions was applied to a sample of 43 first year medical students to illustrate the procedure. (SLD)

Approaches to the determination of cut-scores have used threshold, normal ogive, linear and discrete utility functions. These approaches are examined by investigating conditions on the posterior, likelihood and utility functions required for setting cut-scores in a Bayesian approach. (Author/JKS)

Use of linear combinations of Fisher's "z" transformations as a combined test for the common correlation parameter based on "k" independent sample correlations has been previously studied. This article considers additional "z" additive properties and methods of combining independent studies when planning the number of…