An extended marginal homogeneity model is introduced for the analysis of square contingency tables with the same ordinal row and column classifications. The model hypothesizes that the ratio in each column of table delta will exhibit an exponential function of the column. (SLD)

A method is proposed for comparison of distinct partitions of the same set of n objects through a simple cross-product index defined between corresponding entries from two proximity matrices providing particular a priori codings of the within-class and between-class relationships for the partitions. (SLD)

Hierarchical Linear Models (HLM) have been used extensively for value-added analysis, adjusting for important student and school-level covariates such as socioeconomic status. A recently proposed alternative, the Layered Mixed Effects Model (LMEM) also analyzes learning gains, but ignores sociodemographic factors. Other features of LMEM, such as…

A truncated version of the Cauchy distribution is introduced. Unlike the Cauchy distribution, this possesses finite moments of all orders and could therefore be a better model for certain practical situations. One such situation in finance is discussed. Explicit expressions for the moments of the truncated distribution are also derived.

Interval Shift Analysis (ISA) is an adaptation of the linear programming model used to determine maximum benefits or minimal losses in quantifiable economics problems. ISA is applied to pre and posttest score distributions for 43 classes of second graders. (RC)

An integrated overview is provided of selected multiple comparison methods, with an emphasis on the sequentially rejective Bonferroni (SRB) test and its modifications. Multiple comparisons of means is a frequently used, and yet confusing, method in educational and psychological research. Seven multiple comparison methods are reviewed: (1) the…

Designs for sequential sampling procedures that adapt to cumulative information are discussed. A familiar illustration is the play-the-winner rule in which there are two treatments; after a random start, the same treatment is continued as long as each successive subject registers a success. When a failure occurs, the other treatment is used until…

The purpose of this paper is to demonstrate in detail how the Empirical Bayes (EB) statistical estimation strategy can be applied to an important class of educational research contexts. EB methods are tailored specifically to the analysis of data with a hierarchical structure. For instance, investigators may be interested in discovering how…

Lord's Paradox is analyzed in terms of a simple mathematical model for causal inference. The resolution of Lord's Paradox from this perspective has two aspects. First, the descriptive, non-causal conclusions of the two hypothetical statisticians are both correct. They appear contradictory only because they describe quite different aspects of the…

Configural frequency analysis (CFA), a new method for identifying types, is illustrated numerically. Relations to latent class analysis and to factor analysis are discussed. It is suggested to use CFA as a type-defining method instead of factor analysis if the variables are linked not only by first but also by higher-order associations. (RC)

Emphasizing the measurement of causal effects to arrive at a better understanding of the causal mechanisms involved in statistical theory, a mathematical model for causal inferences in prospective studies is developed and then applied to retrospective case-control studies. Before developing the model, causal agents are delineated, and causal…

This research project addresses a series of methodological and theoretical statistical problems in the analysis of categorical data using loglinear and logistic response models, which grow directly out of problems in the study of the American educational system, and in basic educational research. The project focuses on the adaptation and…

In an attempt to bridge the gap between academic understanding and practical business use, the Box-Jenkins technique of time series analysis for forecasting future events is presented with a minimum of mathematical notation. The method is presented in three stages: a discussion of traditional forecasting techniques, focusing on traditional…

A basic description of the Rasch model and a brief review of the work previously done on the model is related. Simulated data was used to test goodness of fit to the Rasch model. It was found that data with near perfect fit to the Guttman model provides perfect fit to the Rasch model, though a perfect Guttman scale collapses. Random data also…

The behavior of focus samples central to the multiple-look model of Trabasso and Bower is examined by three methods. First, exact probabilities of success conditional upon a certain brief history of stimulation are determined. Second, possible states of the organism during the experiment are defined and a transition matrix for those states…