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…

Several steps are taken to develop methods for analyzing systems that involve probabilistic causation. The basic ideas and distinctions are illustrated for systems with dichotomous variables. It is shown that these basic ideas have analogous counterparts in causal systems with continuous variables. By using a generalized conditional probability…

This paper identifies the need for a new theory of information and develops a mathematical model which distinguishes between: (1) data, as directly observable facts; (2) information, as structured collections of data; and (3) knowledge, as methods of using information. The model is based on the ideas of the binary relational model and uses the…

An algebraic definition of time differentiation is presented and used to relate independent measurements of position and velocity. With this, students can grasp certain essential physical, geometric, and algebraic properties of motion and differentiation before undertaking the study of limits. (Author)

This paper reanalyzes the Hansen-Weisbrod-Pechman debate concerning the equity effects of subsidized tuition for higher education. It presents an intergeneration model of income distribution, including educational effects. This model is used to analyze issues in the debate over equity effects. It yields a measure (equity measure) of the…

The major reasons which seem to be preventing operations research from achieving its potential and fulfilling the expectations of its proponents in library management are explored. (Author)

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)

False drops occur in a system of random superimposed coding for edge-notched, punched, and feature cards. Formulae for the false dropping fraction are derived, and figures and tables are given for the calculated values in the most popular scheme. (Author/LS)

The characteristics of the stratified mixed binomial are reviewed and the adequacy of the simple binomial model for statistical inference when data are of stratified mixed binomial origin is examined using illustrative numerical examples. (Editor)

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…