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…

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.

Of California's 6.3 million public school students in 2006-07, 1.6 million (25%) were considered English learners (EL). Although the vast majority of ELs in the state are Spanish-speaking, more than 50 languages are represented in the state's EL population. English learners are distributed throughout the state and across grade levels, with the…

Using fiscal data provided by the finance office of the school district, and personnel data obtained from the California Basic Education Data System maintained by the California Department of Education (CDE), the authors present analyses to provide a foundation for local policymakers that may be used to assess whether there are inequities in the…

The purpose of this research was to study effects of teaching activities using team learning with different and non-different major subjects on innovative knowledge creation of undergraduate students. The subjects were 14 undergraduate students registered in Technology Activities course (2726311), faculty of Education, Chulalongkorn University.…

Quantiles for finite mixtures of normal distributions are computed. The difference between a linear combination of independent normal random variables and a linear combination of independent normal densities is emphasized. (Contains 3 tables and 1 figure.)

We present empirical data showing that the relative frequency with which a verb normally appears in a syntactic construction predicts young children's ability to remember and repeat sentences instantiating that construction. Children aged 2;10-5;8 years were asked to repeat grammatical and ungrammatical sentential complement sentences (e.g., "I…

This paper is a personal exploration of where the ideas of "distribution" that we are trying to develop in students come from and are leading to, how they fit together, and where they are important and why. We need to have such considerations in the back of our minds when designing learning experiences. The notion of "distribution" as a lens…

This study investigated the benefits of creating item "testlets" or "parcels" in the context of structural equation modeling confirmatory factor analysis (CFA). Testlets are defined as groups of items related to a single content area that is developed as a unit. The strategy is illustrated using data from the administration of…