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…

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)…

Presented is a technical report concerning the use of a mathematical model describing certain aspects of the duplication and selection processes in natural genetic adaptation. This reproductive plan/model occurs in artificial genetics (the use of ideas from genetics to develop general problem solving techniques for computers). The reproductive…

This volume is designed for teachers preparing to teach upper elementary students using the Comprehensive School Mathematics Program (CSMP) curriculum. It begins with a discussion of the importance of graph theory in mathematics and science. A mathematical development of graph-theoretic concepts and theorems is presented, followed by a set of…

The paper examines a longitudinal model of a manpower system in which the demands for effective manpower are determined by the state of a finite Markov chain, and there are delays in training an adequate supply of effective manpower. An operational method of calculating optimal appointment policies is presented. This calculation can in turn be…

This mathematical programing model was developed to provide the State Board of Education with complete information for evaluating decisions about the efficient allocation of vocational education funds to local school districts. The model, based on a supply-demand criterion, was tested on a set of occupational training programs within a given Labor…

The rapid rate of technological development and the growing complexity of our society in recent years have renewed the awareness of the importance of higher education. The rapid expansion of the size of higher educational institutions as well as the increased demand for instructional quality emphasize the need for systematic and efficient resource…

The University of California considers the faculty/student ratio a principal determinant of quality. Requests made by the University for new faculty positions are based on the student/faculty ratios proposed by the University in its 5-year program for each campus. Given the forecasts of student enrollments, these proposed ratios determine the…

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…