A procedure was developed within hypothesis-testing logic that allows researchers to support a hypothesis that has traditionally been the statistical or null hypothesis. Four activities involved in attainment of this goal were discussed: (1) development of statistical logic needed to define the sampling distribution associated with the hypothesis…

A general class of regression models for ordered categorised data is developed and discussed. Thier properties are contrasted with log linear models and other methods of analysis. The general problem of fitting by maximum likelihood is discussed and solved. The models are shown to be multivariate extensions of generalised linear models and the…

Fairness or unfairness may be an attribute of a test per se, or of its use, or of its statistical treatment. An hypothetical situation designed to be intrinsically fair and unbiased is used to show that analysis of covariance as a statistical method may introduce bias to the treatment of test scores. In contrast, equipercentile equating methods…

A theoretical model is developed for analysis of intervention effects in multiple autocorrelated time-series which may be classified or blocked two ways. The intervention effect is estimated independently for each series. The estimates are then entered as observations in two-factor analysis of variance with one observation per cell, utilizing a…

The degree of nonorthogonality in a factorial design was systematically increased. Five methods of dealing with nonorthogonality were selected and applied: two were least squares solutions (Method 1 and Method 2); two were approximate solutions (the unweighted means analysis and the method of expected frequencies); and the fifth was the…

Properly manipulated residuals resulting from "status predicting status" regressions constitute a precise and unique measurement of status inconsistency without the definitional and methodological problems and limitations of simple and simultaneous cross-classification techniques associated with the typical "dummy variable regression" approach.…

Faced with a nonstandard, complicated practical problem in statistical inference, the applied statistician sometimes must use asymptotic approximations in order to compute standard errors and confidence intervals and to test hypotheses. This usually requires that he derive formulas for one or more asymptotic sampling variances (and covariances)…

Reported are the results of a study designed to investigate and compare four cluster analytic procedures as potential methods for the analysis of educational data. A secondary objective was to determine whether or not there was some underlying multidimensional structure to a set of mathematics achievement data. The four clustering procedures (Ball…

Human performance reliability for tasks in the time-space continuous domain is defined and a general mathematical model presented. The human performance measurement terms time-to-error and time-to-error-correction are defined. The model and measurement terms are tested using laboratory vigilance and manual control tasks. Error and error-correction…

Generally, ratings have notoriously low inter-rater reliabilities. Because of differences in orientation, background, and expectations, ratings are seldom made from the same point of reference; thus, many types of error mask the true rating variance. Guilford's technique identified most types of constant error by analysis of variance and then…

The applicability of a mathematical theorem designed to trace causality of a three-variable path that consists of an initial cause variable, an intermediate variable, and a final-effect variable with control over other system variables is evaluated. The formula was used with a horizontal rather than a normal distribution, as had been done in an…

This publication is a discussion of the concept of an educational production function, a mathematical formulation of the relationship between inputs and outputs in education. A description of how a production function can direct decision making toward economic efficiency precedes a theoretical discussion of the nature of actual estimation. Several…

Checking of parametric assumptions is an often ignored step in the inferential process. A misconception regarding symmetry (one aspect of "robustness") is prevalent: that in nonsymmetric distributions the mean and median are always non-coincidental. It is to this fallacious point that the discussion is directed. A generally accepted index of…

An experimental study of the efficiency of human information processing is based on the Bayesian model for simple hypothesis testing with fixed binomial sampling. Each of 60 subjects is analyzed with separate ANOVAs focusing on two efficiency variables. Sample size and critical value are also analyzed. Subjects show very different utilization of…

A scaling technique known as the Method of Reciprocal Averages has been in use since the early 1930's. This technique yields a set of item response weights for a psychological inventory which maximizes the internal consistency of the inventory for a group of subjects. Although the technique has been used for many years, its mathematical…