Understanding large-scale patterns in student course enrollment is a problem of great interest to university administrators and educational researchers. Yet important decisions are often made without a good quantitative framework of the process underlying student choices. We propose a probabilistic approach to modelling course enrollment…

A diverse group of 20 high school students from four states in the US were individually provided with an engineering design challenge. Students chosen were in capstone engineering courses and had taken multiple engineering courses. As students considered the problem and developed a solution, observational data were recorded and artifacts…

In this paper, we show that for some structural equation models (SEM), the classical chi-square goodness-of-fit test is unable to detect the presence of nonlinear terms in the model. As an example, we consider a regression model with latent variables and interactions terms. Not only the model test has zero power against that type of…

Current descriptions of results from hierarchical linear models (HLM) and hierarchical generalized linear models (HGLM), usually based only on interpretations of individual model parameters, are incomplete in the presence of statistically significant and practically important "slopes as outcomes" terms in the models. For complete description of…

In an attempt to bridge the gap between academic understanding and practical business use, the Box-Jenkins technique of time series analysis for forecasting future events is presented with a minimum of mathematical notation. The method is presented in three stages: a discussion of traditional forecasting techniques, focusing on traditional…

Recent mathematical descriptions of Bradford's distribution, and a new formulation that provides a more accurate estimation of the total number of papers and sources on a given scientific subject are presented. (Author/MBR)

Presented is an example meant to enable students with a scant mathematical education to grasp the meaning of the limit of the binomial distribution. (Author/TG)

Reports a solution to the problem of providing annual grade enrollment projections by use of an exponential smoothing model. (Author)

In experiments with paired comparisons, judges are occasionally allowed to express indifference between alternatives. For the analysis of such data, models for paired comparisons with ties are needed. Several models with tie parameters are reviewed. All are extensions of the basic models of L. L. Thurstone (1927) and R. A. Bradley and M. E. Terry…

This study attempts to determine which media-exposure models available today are the best. A survey of the literature of the last 20 years is used to provide the basis for assessment of the state of the art of media planning and to draw distinctions between the implicit, naive, subjective, and sophisticated media-exposure models. Discussion of the…

Results of a comparative study of F and Q tests, in a randomized block design with one replication per cell, are presented. In addition to these two procedures, a multivariate test was also considered. The model and test statistics, data generation and parameter selection, results, summary and conclusions are presented. Ten tables contain the…

Presents two models for statistically analyzing occupational mobility. The models show how the destination distribution is shifted for each shift of one or more steps on the scale of occupational origins. (Author/AV)

A two-year study that attempted to measure patterns of pupil attributions for success and failure in mathematics is reviewed. An attribution pattern variable (ATTPAT) was created to categorize individuals studied into three groups. The first group had an attribution pattern thought to lead to generalized low expectancies for success. Students…

This paper provides a survey of models for the analysis of individual growth data emphasizing the problems posed by serial or time dependence in the application of polynomial regression models. The concepts of serial correlation and autoregressive models are illustrated. It is demonstrated that standard inference procedures may be quite misleading…

The use of subjective probability as a theoretical model for enrollment forecasting is proposed, and the results of an application of subjective probability to enrollment forecasting at the University of Toledo are reported. Subjective probability can be used as an enrollment forecasting technique for both headcount and full-time equivalent using…