This article describes how a group of fifth-grade mathematics students measured irregularly shaped objects using geometric probability theory. After learning how to apply a ratio procedure to find the areas of familiar shapes, students extended the strategy for use with irregularly shaped objects, in this case, leaves. (Contains 2 tables and 8…

This article illustrates how teachers can use the Harry Potter book series to teach linear modeling and probability to their students. (Contains 2 tables and 4 figures.)

Previous research has shown that--due to the extensive attention spent to proportional reasoning in mathematics education--many students have a strong tendency to apply linear or proportional models anywhere, even in situations where they are not applicable. This phenomenon is sometimes referred to as the "illusion of linearity". For example, in…

To assess item dimensionality, the following two approaches are described and compared: hierarchical generalized linear model (HGLM) and multidimensional item response theory (MIRT) model. Two generating models are used to simulate dichotomous responses to a 17-item test: the unidimensional and compensatory two-dimensional (C2D) models. For C2D…

Rating scales are commonly used to study voice quality. However, recent research has demonstrated that perceptual measures of voice quality obtained using rating scales suffer from poor interjudge agreement and reliability, especially in the midrange of the scale. These findings, along with those obtained using multidimensional scaling (MDS), have…

Approximately 9 out of 10 high school students who have access to a home computer use that computer to complete school assignments. Do these home computers, however, improve educational outcomes? Using the Computer and Internet Use Supplement to the 2001 Current Population Survey, I explore whether access to home computers increases the likelihood…

Type I error rates were examined for several fit indices available in GGUM2000: extensions of Infit, Outfit, Andrich's X(2), and the log-likelihood ratio X(2). Infit and Outfit had Type I error rates much lower than nominal alpha. Andrich's X(2) had Type I error rates much higher than nominal alpha, particularly for shorter tests or larger sample…

Prior work indicates that substance use is related to adolescent marriage. We describe two different processes that may account for this relationship and hypothesize patterns of association that would be consistent or inconsistent with each. Using data from a study that followed west coast youth from 7th grade to young adulthood N3,324, we…

The effect of Catholic religiosity as indicated by church attendance on the demand for Catholic schooling at the primary and secondary levels is estimated. It is shown that parents' religiosity has a large effect on the probability that their children attend Catholic schools. Furthermore, estimates of bivariate probit models indicate that parents'…

This paper focuses on whether running away from adolescent residential care facilities is related to having off grounds passes with an adult resource. It was hypothesized that as off grounds passes increased in frequency and duration, runaway behavior would decrease in frequency and duration. Data were collected from two hundred closed client…

This article considers the problem of estimating dynamic linear regression models when the data are generated from finite mixture probability density function where the mixture components are characterized by different dynamic regression model parameters. Specifically, conventional linear models assume that the data are generated by a single…

A hotly debated topic in oropharyngeal dysphagia is the Clinical Swallowing Examination's (CSE) importance in clinical practice. That debate can profit from the application of evidence-based medicine's (EBM) principles and procedures. These can guide both appropriate data collection and interpretation as will be demonstrated in the present report.…

This study examined the relationship between self-reported frequency of condom use (by self or partner during the past 6 months and lifetime), locus of control, self-efficacy, and future time orientation among African American college students who were single and sexually active during the past year. Data were collected from 106 undergraduate…

Three basic theorems concerning expected values and variances of sums and products of random variables play an important role in mathematical statistics and its applications in education, business, the social sciences, and the natural sciences. A solid understanding of these theorems requires that students be familiar with the proofs of these…

The data discussed in this paper are from the television game show "Friend or Foe", and can be used to examine whether age, gender, race, and the amount of prize money affect contestants' strategies. The data are suitable for a variety of statistical analyses, such as descriptive statistics, testing for differences in means or proportions, and…