Two measures of association between sets of variables have been proposed for set correlation: the proportion of generalized variance, and the proportion of additionive variance. Because these measures are strongly positively biased, approximate expected values and estimators of these measures are derived and checked. (Author/BW)

Learnability theory is an attempt to illuminate the concept of learnability using a mathematical model of learning. Two models of learning of categorial grammars are examined here: the standard model, in which sentences presented to the learner are flat strings of words, and one in which sentences are presented in the form of functor-argument…

This Monte Carlo study was designed to investigate empirically the efficacy of three statistical strategies for estimating the relationships in extreme group designs in terms of estimation of correlation, power and mean square error for the correlation. Alf and Abrahams's "covariance information statistic" proved to be the best strategy.…

Problems which can be solved or partially solved by the Gregory Interpolation Formula are presented. The formula is explained and applied to three problems. (MNS)

To modify least squares estimators so that outliers arising from heavy-tailed distributions will have less influence, a robust coefficient of kurtosis, which avoids the quartic effect, is described. Aspects of Pearson's and Fisher's kurtosis coefficients are compared in the procedure. (Author/CM)

Rajaratnam, Cronbach and Gleser's generalizability formula for stratified-parallel tests and Raju's coefficient beta are generalized to estimate the reliability of a composite of criterion-referenced tests, where the parts have different cutting scores. (Author/GK)

Assessed the validity of short forms that reduce the number of items within subtests rather than the number of subtests. Used data from the standardization samples for the Wechsler Intelligence Scale for Children, Wechsler Adult Intelligence Scale, Wechsler Preschool and Primary Scale of Intelligence, WISC-Revised, and WAIS-Revised. (Author)

It is suggested that error of measurement cannot be routinely incorporated into the "error term" in statistical tests, and that the reliability of test scores does not have the simple relationship to statistical inference that one might expect. (Author/GK)

A human interest account of the discovery of a mathematical formula is given. (Author/MK)

Suggests that ordinal and ratio criteria for equity are independent of one another, but that a plausible mathematical definition of equity must satisfy both criteria under all outcome/input ratio situations. Demonstrates that a modification of the Harris linear formula for equity meets these criteria. (Author/RD)

Maxwell's equation are solved for an inhomogeneous medium which has a coordinate-dependent dielectric function. The problem and its solutions are given in a format which should make it useful as an intermediate or advanced level problem in an electrodynamics course. (Author/SK)

An algorithm for multiplying natural numbers is described. The algorithm provides a chance for some unusual drill and might serve as an enrichment topic. (MK)

The derivation of a formula relating areas of triangles formed by cutting the corner of a cube is given. (MK)

Uses an historical analogy with Archimedes' problem concerning the volume of his king's golden crown to illustrate the evaluation problem for document and reference retrieval systems. Various methods that have been developed since 1950 to measure retrieval effectiveness are described, and utility measure formulas are provided. (JD)

Equations for estimating the value of the multiple correlation coefficient in the population underlying a sample and the value of the population validity coefficient of a sample regression equation were investigated. Results indicated that cross-validation may no longer be necessary for certain purposes. (Author/MH)