In this paper, we consider some combinatorial and statistical aspects of the popular "Powerball" lottery game. It is not difficult for students in an introductory statistics course to compute the probabilities of winning various prizes, including the "jackpot" in the Powerball game. Assuming a unique jackpot winner, it is not difficult to find the…

Monte Carlo computational experiments reveal that the ability to discriminate between first- and second-order kinetics from least-squares analysis of time-dependent concentration data is better than implied in earlier discussions of the problem. The problem is rendered as simple as possible by assuming that the order must be either 1 or 2 and that…

A system of education is a unique social institution, the purpose of which is to develop and multiply human capital. Based on the education system it is possible to judge the situation in the country and society not only at the present time but also in the future. A system of education also should be seen as an ideological institution: it produces…

In current curriculum materials for middle school students in the US, data and chance are considered as separate topics. They are then ideally brought together in the minds of high school or university students when they learn about statistical inference. In recent studies we have been attempting to build connections between data and chance in the…

In 3 studies, participants viewed sequences of multiattribute objects (e.g., colored shapes) appearing with varying frequencies and judged the likelihood of the attributes of those objects. Judged probabilities reflected a compromise between (a) the frequency with which each attribute appeared and (b) the ignorance prior probability cued by the…

Tests of mean equality proposed by Alexander and Govern (1994) and Tsakok (1978) were compared to the well-known procedures of Brown and Forsythe (1974), James (1951), and Welch (1951) for their ability to limit the number of Type I errors in one-way designs where the underlying distributions were nonnormal, variances were nonhomogeneous, and…

RESGEN is a computer program designed to generate simulated latent trait distributions and then dichotomous or polytomous item responses based on item response models. The latent trait distributions can be univariate or multivariate normal, log-normal, uniform, or gamma. The item response models utilized in this program may have characteristics…

Although an analysis of covariance (ANCOVA) allows for the removal of an uncontrolled source of variation that is represented by the covariates, this "correction," which occurs with the dependent variable scores is unfortunately seen by some as a blanket adjustment device that can be used with an inadequate amount of consideration for…

Previous research has demonstrated particular inadequacies in conventional methods used to identify outlier cases in bivariate regression models. Only through a combination of methods can one detect all of the deviant points potentially overinfluencing a regression model's parameters. This paper investigates whether a range of data points might…

The reports that teachers receive from the Portland (Oregon) Public Schools Achievement Level Testing Program are planned to help them to see how each individual student is doing, which students need help, and how the class is performing as a whole. The information enables teachers to focus on special needs and problem areas, and also to see an…

The random variable p and its functions figure in several "tests of combined significance," meta-analysis summaries based on sample significance values, and ps have been used singly, as well as in other tests for evaluating the outcomes of individual research studies. In this work, asymptotic distributions of the sample one-sided…

This document reviews "The Collected Works of George E. P. Box," edited by G. C. Tiao. The two-volume collection is divided into five parts. Each part is prefaced with an introduction by a statistical researcher giving his view of the motivation and highlights of the papers presented. The 16 papers in Part 1 on statistical inference,…

The present investigation developed power curves for two parametric and two nonparametric procedures for testing the equality of population variances. Both normal and non-normal distributions were considered for the two group design with equal and unequal sample frequencies. The results indicated that when population distributions differed only in…

Examines relationships among the parameters of the Zipf size-frequency distribution as well as its sampling properties. Highlights include its importance in bibliometrics, tables for the sampling distribution of the maximal value of a finite Zipf distribution, and an approximation formula for confidence intervals. (Author/LRW)

Preliminary results of a survey of 10-year-old children (N=12.905) given a variety of educational and cognitive tests relevant to diagnosis of dyslexia have shown that distributions of scores are incompatible with the hypothesis of normal variation, suggesting that dyslexia involves some kind of anomaly. (Author/DB)