"The Condition of Education 2018" is a congressionally mandated annual report summarizing the latest data on education in the United States. This report is designed to help policymakers and the public monitor educational progress. This report contains indicators on the state of education in the United States, from prekindergarten through…

The mean and variance of some continuous distributions, in particular the exponentially decreasing probability distribution and the normal distribution, are considered. Since they involve integration by parts, many students do not feel comfortable. In this note, a technique is demonstrated for deriving mean and variance through differential…

Test statistics based on the assumption that test scores are interval rather than ordinal quality data are questioned. New statistical techniques which do not rely on this assumption are presented. (JKS)

This paper provides a brief review of the concepts of confidence intervals, effect sizes, and central and noncentral distributions. The use of confidence intervals around effect sizes is discussed. A demonstration of the Exploratory Software for Confidence Intervals (G. Cuming and S. Finch, 2001; ESCI) is given to illustrate effect size confidence…

While violation of the homogeneity of variance assumption has received considerable attention, violation of the assumption of normally distributed data has not received as much attention. As a result, researchers may have the mistaken impression that as long as the assumptions of independence of observations and homogeneity of variance are…

Two multivariate probability distributions, a generalized beta distribution and a generalized F distribution, are derived. Formulas for the moments of these distributions are given and an example of the bivariate generalized beta is presented. (Author/JKS)

DIMTEST is a nonparametric statistical test procedure for assessing unidimensionality of binary item response data that uses the T-statistic of W. F. Stout (1987). This study investigates the performance of the T-statistic with respect to different shapes of ability distributions and confirms its nonparametric nature. (SLD)

Outlines the multivariate latent distribution specification and the corresponding interpretation issues. Also shows the univariate formulation and some alternative parameterizations that are useful in the estimation phase. Illustrates the procedures through an application to student ratings data. (SLD)

A k-dimensional multivariate normal distribution is made discrete by partitioning the k-dimensional Euclidean space with rectangular grids. The probability integrals over the partitioned cubes forms a k-dimensional contingency table with ordered categories. A loglinear model with main effects plus two-way interactions provides an approximation for…

Examined two ways of measuring the gap between two cumulative distribution functions (CDFs), vertical and horizontal distance. Demonstrated how these two approaches can lead to contradictory conclusions about small changes in gaps using real data from the National Assessment of Educational Progress. (SLD)

Examines significant studies, published from 1934 through 1987, which have contributed to an understanding of three central concerns in the specialty associated with Bradford's law: the appropriate formulation for Bradford's law, the parameters of the Bradford distribution, and the Bradford distribution's relationships to other distributions. (79…

Describes informetric distributions as a family of regularities found to describe a wide range of phenomena both within and outside of the information sciences. Highlights include Bradford's Law of Scattering; Leimkuhler Variant; Lotka's Law; Zipf's Law; Pareto's Law; and a discussion of consequences for the social sciences. (22 references) (LRW)

Presents an application of the EM-algorithm to two problems of estimation and testing in a multivariate normal distribution with missing data. The two models are tested applying the log-likelihood ratio test. Solves the problem of different and nonmonotone patterns of missing data by introducing suitable transformations and partitions of the data…

Examined the sampling distributions of equating coefficients produced by the characteristic curve method for tests using graded and nominal response scoring using simulated data. For both models and across all three equating situations, the sampling distributions were generally bell-shaped and peaked, and occasionally had a small degree of…

Provides a practical introduction to methods of constructing confidence intervals for multiple and partial "R" squared and related parameters in multiple regression models based on noncentral distributions. Illustrates software use (e.g. the Statistical Package for Social Studies) for confidence intervals and discusses measures of effect…