Argues the usefulness of algebraic and topological mathematical models and general principle formulation for educational research. Applies an algebraic model to relate learning to the pace of instruction. Formulates two broad principles: the Quantitative and Qualitative Teaching Principles (more teaching produces more learning; and learning is…

THIS REPORT PRESENTS A DISCUSSION OF 2 TECHNIQUES WHICH CAN BE USED TO REPRESENT AND INTERPRET MULTIVARIATE STATISTICAL SYSTEMS WHEN IT IS FELT THAT THERE ARE CAUSAL RELATIONS BETWEEN SOME OF THE VARIABLES. THE BASIC TECHNIQUE IS PATH ANALYSIS AND THE OTHER IS ITS EXTENSION THROUGH THE USE OF RECURSIVE SYSTEMS OF EQUATIONS. THE ANALYSIS IS…

The correction for attenuation formulas for partial, multiple, and canonical correlation coefficients are discussed and the effects of measurement errors on these statistics are explored. The notation is standardized and the derivation extended where appropriate. It is shown that as the reliabilities of the predictors become more disparate, the…

The problem of the comparability of change scores is investigated. Change quotients and residual change scores are evaluated as alternative approaches and methods for estimating the true change and true score residual, the reliability of change scores and residuals, and procedures for constructing confidence intervals for residuals are explored.…

This paper relates educational and psychological statistics to certain "Research Statistical Tools" (RSTs) necessary to accomplish and understand general research in the behavioral sciences. Emphasis is placed on acquiring an effective understanding of the RSTs and to this end they are are ordered to a continuum scale in terms of individual…

An iterative least squares procedure for analyzing the effect of various kinds of intervention in time-series data is described. There are numerous applications of this design in economics, education, and psychology, although until recently, no appropriate analysis techniques had been developed to deal with the model adequately. This paper…