Instead of reserving the study of probability and statistics for special fourth-year high school courses, the Common Core State Standards for Mathematics (CCSSM) takes a "statistics for all" approach. The standards recommend that students in grades 6-8 learn to summarize and describe data distributions, understand probability, draw…

The effect of simulation-based probability teaching on the prospective teachers' inference skills has been examined with this research. In line with this purpose, it has been aimed to examine the design, implementation and efficiency of a learning environment for experimental probability. Activities were built on modeling, simulation and the…

On the basis of the statistical concept of waiting time and on computer simulations of the "probabilities of nonoccurrence" (p. 457) for random sequences, Hahn and Warren (2009) proposed that given people's experience of a finite data stream from the environment, the gambler's fallacy is not as gross an error as it might seem. We deal with two…

The residuals obtained from fitting a structural equation model are crucial ingredients in obtaining chi-square goodness-of-fit statistics for the model. The authors present a didactic discussion of the residuals, obtaining a geometrical interpretation by recognizing the residuals as the result of oblique projections. This sheds light on the…

A challenging problem in some developing countries such as Nigeria is inadequate training of students in effective problem solving using the core concepts of their disciplines. Related to this is a disconnection between their learning and socio-economic development agenda of a country. These problems are more vivid in statistical education which…

The purpose of these modules is to provide an introduction to the world of probability and statistics to accelerated mathematics students at the high school level. The materials are centered on the fictional town of Happy Shores, a coastal community which is at risk for hurricanes. Actuaries at an insurance company figure out the risks and…

The online deployment of Technology Engineered online Student Ratings of Instruction (SRIs) by colleges and universities in the United States has dynamically changed the deployment of course evaluation. This research investigation is the fourth part of a post hoc study that analytically and psychometrically examines the design, reliability, and…

Lord's Paradox is analyzed in terms of a simple mathematical model for causal inference. The resolution of Lord's Paradox from this perspective has two aspects. First, the descriptive, non-causal conclusions of the two hypothetical statisticians are both correct. They appear contradictory only because they describe quite different aspects of the…

A basic description of the Rasch model and a brief review of the work previously done on the model is related. Simulated data was used to test goodness of fit to the Rasch model. It was found that data with near perfect fit to the Guttman model provides perfect fit to the Rasch model, though a perfect Guttman scale collapses. Random data also…

Explicit formulas are derived for the asymptotic sampling variances and covariances of the maximum likelihood estimators for factor-analysis parameters in the special case where there is just one common factor. The effect of the number of variables on these variances and covariances is indicated. A formula is given showing to what extent the usual…

A class of tests for normality using the ratio of two estimates of the standard deviation is generalized to provide a class of tests for multivariate normality using a characterization of the multivariate normal. The posers of some of the tests are examined numerically and compared with the power of a recent similar test. (Author)

The statistician has n independent estimates of a parameter he knows is positive, but, as is the case in components-of-variance problems, some of the estimates may be negative. If the n estimates are to be combined into a single number, we compare the obvious rule, that of averaging the n values and taking the positive part of the result, with…

The 30 papers in the area of educational statistics that were presented at the 1972 AERA Conference are reviewed. The papers are categorized into five broad areas of interest: (1) theory of univariate analysis, (2) nonparametric methods, (3) regression-prediction theory, (4) multivariable methods, and (5) factor analysis. A list of the papers…