This analysis of Zipf's law uses an index for the sequence of observed values of the variables in a Zipf-type relationship. Three important properties relating rank, count, and frequency are identified, shapes of Zipf-type curves are described, and parameters of the Mandelbrot-Zipf law are discussed. (Author/LRW)

The overidentification of structural equation models with latent variables is discussed. The use of two- and three-indicator models is not recommended since such models do not allow a testing of the crucial assumption of unidimensionality among indicators in most cases. Models with four or more indicators may be more sensitive to departures from…

The stepwise regression method of selecting predictors for computer assisted multiple regression analysis was compared with forward, backward, and best subsets regression, using 16 data sets. The results indicated the stepwise method was preferred because of its practical nature, when the models chosen by different selection methods were similar…

This paper discusses the principles underlying discriminant analysis and constructs a simulated data set to illustrate its methods. Discriminant analysis is a multivariate technique for identifying the best combination of variables to maximally discriminate between groups. Discriminant functions are established on existing groups and used to…

In research, data sets often occur in which the variance of the distribution of the dependent variable at given levels of the predictors is a function of the values of the predictors. In this situation, the use of weighted least-squares (WLS) or techniques is required. Weights suitable for use in a WLS regression analysis must be estimated. A…

A reduction in agricultural activity in a rural farming community will result in reduced activity in almost every sector of the local economy. The result may be measured in loss of employment and income. This report provides a method to estimate such economic impacts with a minimum of data collection and manipulation. Most of the input data…

Meta-analysis is a technique for combining the summary statistics from previously conducted research studies to indicate the direction of results and provide an index of the magnitude of effect size. This paper focuses on the effect of the violation of the assumption of independence (that the value of any included statistic is in no way…

Examines two classes of production functions in which the long-run competitive equilibrium scale of the firm increases when the relative price of the dominant factor decreases. Compares these with a third class of production functions where the equilibrium scale is independent of the relative price of the dominant factor. (MJP)

Describes class exercises where undergraduates construct and test mathematical models using data and issues related to social security. The students collect data and forecast economic and demographic variables that determine future tax rates. They then discuss government policies that are derived from their models. (MJP)

Uses the various strategies involved in baseball to illustrate basic concepts in game theory. Specifically discusses Willie Mays' base-stealing strategy and how it relates to probability and risk. Reminds students that expected results depend on adopted assumptions. (MJP)

A reanalysis was conducted of Saunier's research (1985) on sources of variation in the National Research Council (NRC) reputational ratings of university faculty. Saunier conducted a stepwise regression analysis using 12 predictor variables. Due to problems with multicollinearity and because of the atheoretical nature of stepwise regression,…

This paper reports the results of a Monte Carlo investigation of Type I errors in the single group repeated measures design where multiple measures are collected from each observational unit at each measurement occasion. The Type I error of three multivariate tests were examined. These were the doubly multivariate F test, the multivariate mixed…

Research investigations on teacher training effects have focused almost exclusively on differences between group means. The present paper suggests that several interesting and important research questions might be answered by examining student variability both within and between classrooms. Student variability might be considered as an outcome to…

A method for drawing inferences from complex samples is based on Rubin's approach to missing data in survey research. Standard procedures for drawing such inferences do not apply when the variables of interest are not observed directly, but must be inferred from secondary random variables which depend on the variables of interest stochastically.…

Two approaches for conceptualizing and estimating a contextual model for analyzing student achievement are the separate equation approach and the single equation approach. The separate equation method determines the relationship between the individual-level independent variable and the individual-level dependent variable within each group. It then…