The problem of rotating a matrix orthogonally to a best least squares fit with another matrix of the same order has a closed-form solution based on a singular value decomposition. The optimal rotation matrix is not necessarily rigid, but may also involve a reflection. In some applications, only rigid rotations are permitted. Gower (1976) has…

A simple, direct condition is formulated for determining the mode(s) of a probability mass function. This condition is then applied to the Poisson and hypergeometric mass functions.

Euler gave a simple method for showing that [zeta](2)=1/1[superscript 2] + 1/2[superscript 2] + 1/3[superscript 2] + ... = [pi][superscript 2]/6. He generalized his method so as to find [zeta](4), [zeta](6), [zeta](8),.... His computations became increasingly more complex as the arguments increased. In this note we show a different generalization…

For the casino game Keno we determine optimal playing strategies. To decide such optimal strategies, both exact (hypergeometric) and approximate probability calculations are used. The approximate calculations are obtained via the Central Limit Theorem and simulation, and an important lesson about the application of the Central Limit Theorem is…

This note describes a procedure for estimating the range restriction component used in correcting correlations for unreliability and range restriction when an estimate of the reliability of a predictor is not readily available for the unrestricted sample. This procedure is illustrated with a few examples. (Contains 1 table.)

This paper introduces the language associated with a polygon microworld called Polygon R&D, which has the mathematical crispness of Logo and has the discreteness and simplicity of a Turing machine. In this microworld, polygons serve two purposes: as agents (similar to the turtles in Logo), and as data (landmarks in the plane). Programming the…

Using computer simulation, the authors assessed the accuracy of J. E. Hunter, F. L. Schmidt, and H. Le's (2006) procedure for correcting for indirect range restriction, the most common type of range restriction, in comparison with the conventional practice of applying the Thorndike Case II correction for direct range restriction. Hunter et…

This article provides technical descriptions of five fixed parameter calibration (FPC) methods, which were based on marginal maximum likelihood estimation via the EM algorithm, and evaluates them through simulation. The five FPC methods described are distinguished from each other by how many times they update the prior ability distribution and by…

Results from nine experiments were analyzed to evaluate the relationship between relative problem completion rates (RPCR) and judgments of time involving mathematics assignments. For each experiment, control assignments contained only target mathematics computation or word problems. Matched experimental assignments contained similar target…

A continuity principle is suggested for scaling of assessment scores from different levels of a multilevel mastery training program. In such training programs students are self-paced and work at levels of tasks appropriate for their levels of performance. The problem addressed in this report concerns the scaling of assessment scores at different…

An elementary arithmetic workbook in whole numbers for speakers of Hmong has an introductory section and a variety of exercises in conceptualizing, writing, spelling, and sequencing numbers from 0 to 999. (MSE)

The data within this publication provide guidelines for planners, engineers and decision-makers at all governmental levels to evaluate cost-effectiveness of alternative wastewater treatment proposals. The processes described include conventional and advanced treatment units as well as most sludge handling and processing units. Flow sheets, cost…

Compares one study in which 5-year-olds and another in which adults quantified random patterns of dots under unlimited exposure duration. Data on operating ranges and rates for subitizing and counting are included. (JMB)

Five activities are presented in this student workbook on using the electronic calculator. Following the directions for using the machine, problems are given on multiplying and dividing, finding percentages, calculating the area of assorted polygons, changing fractions to decimals, and finding squares and square roots. (JH)