The sampling distribution is a common source of misuse and misunderstanding in the study of statistics. The sampling distribution, underlying distribution, and the Central Limit Theorem are all interconnected in defining and explaining the proper use of the sampling distribution of various statistics. The sampling distribution of a statistic is…

The record values of the Pareto distribution, labelled Pareto (II) (alpha, beta, nu), are reviewed. The best linear unbiased estimates of the parameters in terms of the record values are provided. The prediction of the sth record value based on the first m (s>m) record values are obtained. A classical Pareto distribution provides reasonably…

This study compared two approximations for normalizing noncentral F distributions: one based on the square root of the chi-square distribution (SRA), the other derived from a cube root of the chi-square distribution (CRA). The CRA was superior, and generally provided an excellent approximation for noncentral F. (Author/BW)

Demonstrates the use of the Waring distribution as a model for the frequency distribution of scientific productivity. Methods for testing the fit at both ends of the distribution, as well as for estimating the parameters of the distribution and the total number of scientists, are outlined. (16 references) (Author/CLB)

Discusses the interdependencies between parameter estimation and properties of probabilistic models, such as dependency assumptions, binary vs. nonbinary features, and estimation sample selection. An optimum estimation for binary features applicable to information retrieval is defined, a method for computing this estimation using empirical data is…

Statistical methods are presented for studying "correlates of diversity," defined as characteristics of educational organizations that predict dispersion on the dependent variable. Strategies based on exact distribution theory and asymptotic normal approximation are considered. (TJH)

Presents a coordination level matching algorithm to be used in document retrieval systems that incorporate relevance feedback strategies. It is argued that this algorithm may eliminate the need for the frequent reevaluation of documents that is currently found in such systems, and conditions under which reranking is unnecessary are given.…

Previous work on the mathematical and implementation details of the marginalized maximum likelihood estimation procedure is extended to encompass the marginalized Bayesian procedure for estimating item parameters of R. J. Mislevy (1986) and to communicate this procedure to users of the BILOG computer program. (SLD)

The observed probability "p" is the social scientist's primary tool for evaluating the outcome of statistical hypothesis tests. The small-sample accuracy of nonnull asymptotic distributions of several functions of "p" was studied. Implications for use of the approximations are discussed. (SLD)

Modifications are proposed to the recently developed method of comparing one-step M-estimators of location corresponding to two independent groups that provides good control over the probability of Type I error even for unequal sample size, unequal variances, and different shaped distributions. Simulation results reveal cautions required. (SLD)

This paper describes a study, now in progress, of new methods for representing the sampling variability of Mantel-Haenszel differential item functioning (DIF) results, based on the system for categorizing the severity of DIF that is now in place at the Educational Testing Service. The methods, which involve a Bayesian elaboration of procedures…

Describes probabilistic document retrieval systems as a sequential learning process, in which the system learns the parameters of probability distributions describing the frequencies of feature occurrences in relevant and nonrelevant documents. Several techniques for estimating the parameters of distributions are described and the results of tests…

Hierarchical Bayes procedures were compared for estimating item and ability parameters in item response theory. Simulated data sets from the two-parameter logistic model were analyzed using three different hierarchical Bayes procedures: (1) the joint Bayesian with known hyperparameters (JB1); (2) the joint Bayesian with information hyperpriors…

Advances in computer technology are making it possible for educational researchers to use simpler statistical methods to address a wide range of questions with smaller data sets and fewer, and less restrictive, assumptions. This digest introduces computationally intensive statistics, collectively called resampling techniques. Resampling is a…