Data reduction techniques seek to combine variables that account for patterns of variation in observed dependent variables in such a way that a simpler model is available for analysis. Factor analysis is a data reduction technique that attempts to model or explain a set of variables in terms of their associations. To understand why this technique…

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…

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…

Math modeling is currently at the focus of educational methodologists' attention. However, little is known about the extent to which principles of the math modeling lead to methodological fallacies in educational research. The main purpose of this paper is to explore the nature and principles of math modeling and to examine its application in…

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…

A research project developed a computer program for analyzing time series quasi-experimental data. The program generates a nonstationary, integrated moving average time series model; it is used to estimate a parameter which indexes the instantaneous change in level of the time series due to a predesignated treatment. The entire method is based on…

CERTAIN SPECIFIC ASPECTS OF HYPOTHESIS TESTS USED FOR ANALYSIS OF RESULTS IN RANDOMIZED EXPERIMENTS WERE STUDIED--(1) THE DEVELOPMENT OF THE THEORETICAL FACTOR, THAT OF PROVIDING INFORMATION ON STATISTICAL TESTS FOR CERTAIN EXPERIMENTAL DESIGNS AND (2) THE DEVELOPMENT OF THE APPLIED ELEMENT, THAT OF SUPPLYING THE EXPERIMENTER WITH MACHINERY FOR…

Sixteen measures of reliability for two-category nominal scales are compared. Upon correcting for chance agreement, there are only five distinct indices: Fleiss's modification of A-sub-1, the phi coefficient, Cohen's kappa, and two intraclass coefficients. Recommendations for choosing an agreement index are made based on definitions, magnitude,…

The concepts of quantitative and structural change are considered from a multivariate perspective. A hybrid of these two types of change, quantistructural change, is described. (CS)

A method is proposed for detecting influential observations in iterative principal factor analysis. Theoretical influence functions are derived for two components of the common variance decomposition. The major mathematical tool is the influence function derived by Tanaka (1988). (SLD)

The effects of several specification search strategies used with Covariance Structure Modeling to obtain more parsimonious models are examined. The initial models vary in their degree of "correctness." Restricting modifications to those justified by prior theoretical knowledge improves the success of a specification search. (TJH)