The testing of a priori contrasts, post hoc contrasts, and experimental error rates are discussed. Methods for controlling the experimental error rate for a set of a priori contrasts tested simultaneously have been developed by Dunnett, Dunn, Sidak, and Krishnaiah. Each of these methods is discussed and contrasted as to applicability, power, and…

A partial least squares method is described for estimating parameters of linear structural relation models. This method is an extension of Herman Wold's proposal for estimation parameters without distributional assumptions, using some algorithms worked out by Paul Horst. The method (LISPLS) determines a different number of latent variables from…

The robustness of the Johnson-Neyman technique and analysis of covariance (ANCOVA) to violations of assumptions of homoscedasticity and homogeneity of variance was tested through the use of Monte Carlo computer procedures. The study simulated a one-way, fixed-effects analysis with two treatment groups, one criterion, Y, and one covariate, X. Five…

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…

Some of the problems and techniques involved in manpower forecasting are discussed. This non-technical introduction to the field aims at reducing fears of data manipulation methods and at increasing respect for conceptual, logical, and analytical issues. The major approaches to manpower forecasting are explicated and evaluated under the headings:…

This report contains five papers which describe mathematical models of the educational system as it relates to economic growth. Experimental applications of the models to particular educational systems are discussed. Three papers, by L. J. Emmerij, J. Blum, and G. Williams, discuss planning models for the calculation of educational requirements…

As part of a project designed to construct a mathematical model of the operation of an academic library, a research team determined the usefulness of a quantitative approach to making decisions about the number of copies of each item that a university library should provide. Using the reserve collection of the University of Lancaster Library as a…

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…

An interesting econometric problem is to decide whether any given state in the budget process is an example of the political or the bureaucratic model of budgeting. The current paper presents a method of deciding this question and then uses it to study local governmental spending on education. The method is based on the important difference…

This is a collection of articles dealing with mathematical applications for use by high school teachers and students. The articles are intended to illustrate several themes: (1) how mathematics is applied via construction of mathematical models; (2) the various types of activities in applied mathematics; (3) the role of pure mathematics in applied…

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…

A mathematical model of the Ph.D. scientist labor market demonstrates that subsidies of graduate training can be more cost effective than higher wages if the supply of doctorates is substantially more responsive to $1000 of early subsidy than to higher future wages with a present discounted value of $1000. Whether this is true is an unsettled…

Tenure fraction has become recognized as an important factor to be taken into account in the administration of institutions of higher education, but there is danger that pursuit of lower fractions per se may lead to actions that unnecessarily weaken the institution or its educational programs. With the aid of an extremely simple mathematical model…

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…