A new methodology is proposed for the simultaneous reduction of units, variables, and occasions of a three-mode data set. Units are partitioned into a reduced number of classes, while, simultaneously, components for variables and occasions accounting for the largest common information for the classification are identified. The model is a…

This note describes a method for evaluating the sums of the m -th powers of n consecutive terms of a general arithmetic sequence: { S[subscript m] = 0, 1, 2,...}. The method is based on the use of a differential operator that is repeatedly applied to a generating function. A known linear recurrence is then obtained and the m-th sum, S[subscript…

This paper considers the problem of analysis of correlation coefficients from a multivariate normal population. A unified theorem is derived for the regression model with normally distributed explanatory variables and the general results are employed to provide useful expressions for the distributions of simple, multiple, and partial-multiple…

Following a pretest, 8 participants who were unfamiliar with algebraic and trigonometric functions received a brief presentation on the rectangular coordinate system. Next, they participated in a computer-interactive matching-to-sample procedure that trained formula-to-formula and formula-to-graph relations. Then, they were exposed to 40 novel…

Libraries have always had to determine how to allocate resources for the purpose of purchasing materials. As budgets shrink and as information becomes more open, objective methods of allocating funds become more attractive. This Clip Note examines the use of formulas in the smaller institution academic environment. It identifies elements used in…

This computer software program helps to make classroom worksheets, take home assignments, and school mathematics tests easy to design and manufacture. The accompanying printed teaching guide provides technical information for setting up and using the program, along with sample worksheets and instructions on how to create them using the software.…

A pivotal theorem which is of critical importance to statistical inference in probability and statistics is the Central Limit Theorem (CLT). The theorem concerns the sampling distribution of random samples taken from a population, including population distributions that do not have to be normal distributions. This paper contains a brief history of…

This study investigates the accuracy of the Woodruff-Causey technique for estimating sampling errors for complex statistics. The technique may be applied when data are collected by using multistage clustered samples. The technique was chosen for study because of its relevance to the correct use of multivariate analyses in educational survey…

Representing the work of a Task Force on Community College Finance established by the California State Legislature, this report recommends criteria and standards for the implementation of a new program-based funding mechanism for the state's community colleges. After reviewing the legislative mandate for the implementation of program-based…

This courseware evaluation rates the "Introduction to Nursing Diagnosis" program developed by J.B. Lippincott Co. (The program--not included in this document--is a tutorial for second-year nursing students; it presents diagnosis as a mathematical formula). Part A describes the program in terms of subject area (allied health, nursing) and hardware…

The study looks at sources of income, both legal and practical, identifies reasonable levels for library support, compares sources of governmental revenue and the costs of providing adequate library services, and develops mathematical formulas that can be used as measures of the city's or county's ability to support library services. The study…

Five distribution-free alternatives to parametric analysis of covariance (ANCOVA) are presented and demonstrated using a specific data example. The procedures considered are those suggested by Quade (1967); Puri and Sen (1969); McSweeney and Porter (1971); Burnett and Barr (1978); and Shirley (1981). The results of simulation studies investigating…

This project had three major goals: (1) investigate the extent to which introductory physics students misuse or misunderstand formulas; (2) catalogue the typical ways in which they do this; and (3) begin the larger task of identifying key types of knowledge that successful problem solvers use to give formulas meaning. Exploratory interviews and…

A Monte Carlo study was conducted to estimate the efficiency of and the relationship between five equations and the use of cross validation as methods for estimating shrinkage in multiple correlations. Two of the methods were intended to estimate shrinkage to population values and the other methods were intended to estimate shrinkage from sample…

The EM algorithm is used to derive maximum likelihood estimates for item parameters of the two-parameter logistic item response curves. The observed information matrix is then used to approximate the covariance matrix of these estimates. Simulated data are used to compare the estimated and actual item parameters. (Author/BW)