A model permitting construction of algorithms for the polynomial conjoint analysis of similarities is presented. This model, which is based on concepts used in nonmetric scaling, permits one to obtain the best approximate solution. The concepts used to construct nonmetric scaling algorithms are reviewed. Finally, examples of algorithmic models for…

The purpose of this paper is to define the framework within which empirical investigations of probabilistic grammars can take place and to sketch how this attack can be made. The full presentation of empirical results will be left to other papers. In the detailed empirical work, the author has depended on the collaboration of E. Gammon and A.…

A unit on probability and statistics was introduced into 18 ninth-grade general mathematics classes. The effects of this unit on teacher attitude, student attitude, and student achievement in several selected mathematical areas were investigated. The experimental group of 18 classes and a comparison group of 17 classes were tested before and after…

These materials were written with the aim of reflecting the thinking of Cambridge Conference on School Mathematics (CCSM) regarding the goals and objectives for school mathematics. Presented are plans for teaching 23 probability lessons in the elementary grades at Hancock School, Lexington, Massachusetts. The discovery approach was utilized by the…

When analysis of variance is used, statistically significant differences may or may not be of practical significance to educators. A large part of the problem is due to the fact that a "zero difference" null hypothesis can always be rejected statistically if the sample size is large enough. If, however, a method based on the noncentral F…

This booklet, part of a series of four which provide problems in probability and statistics for the secondary school level, is aimed at aiding the student in developing models as structure for data and in learning how to change models to fit real-life problems. Twelve different problem situations arising from biology, business, English, physical…

This guidebook on minimum content for a study of probability and its applications was designed for the student who has mastered second-year algebra. Covered in this booklet are sample spaces; tree diagrams, permutations, combinations, probability concepts and applications; and game theory. The course goals and performance objectives are specified,…

This paper presents an index of goodness-of-fit for comparing m models over n trials. The index allows for differentiated weighting of the trials as to their importance in the comparison of the models. Several possible weighting schemes are suggested and the conditions on the weights which assure asymptotic normality of the index distribution are…

In order to investigate the use of strategies in a game-playing computer program, "Gammon," a computer program that plays Backgammon, was developed. It focuses on the play of a given strategy, as well as the process of strategy selection, and examines the concept of strategy as an integrating and driving force in the play of a game. A…

This booklet contains some 80 problems in mathematics suitable for computer solution. The problems range from very simple to complex. Problems have been included from most mathematic disciplines, including number theory, analytical geometry, probability and statistics, trigonometry, equations, and sequence and limits. For the most part these…

In this report, the author suggests changes in the treatment of overhead costs by hypothesizing that "the effectiveness of standard costing in planning and controlling overhead costs can be increased through the use of probability theory and associated statistical techniques." To test the hypothesis, the author (1) presents an overview of the…

This report presents the results of research that examined widely diverse decision problems and attempted to specify their common behavior elements. To take into account the psychological complexity of most real-life decision problems, and to develop a tentative organization of decision behavior that will embrace the many, highly diverse types of…

Unit 18 in the SMSG secondary school mathematics series is a student text covering the following topics: logarithms and exponents; trigonometry; the system of vectors; polar form of complex numbers; sequences and series; permutations, combinations, and the binomial theorem; and algebraic structures. (DT)

The development of an index reflecting the probability that the observed correspondence between multiple choice test responses of two examinees was due to chance in the absence of copying was previously reported. The present paper reports the implementation of a statistic requiring less restrictive underlying assumptions but more computation time…

Tables of life expectancy can provide data for use in a great variety of problems related to probability theory. (SD)