This paper analyzes the government expenditures as the percentage of gross domestic product across countries of the European Union. There is a statistical model based on Z-score, whose aim is to calculate how much each EU country deviates from the average value. The model shows that government expenditures on education vary significantly between…

When fitting hierarchical regression models, maximum likelihood (ML) estimation has computational (and, for some users, philosophical) advantages compared to full Bayesian inference, but when the number of groups is small, estimates of the covariance matrix [sigma] of group-level varying coefficients are often degenerate. One can do better, even…

Background: Evaluating diversity, inclusivity, and equity remains both a prevalent topic in education and a difficult challenge for most evaluators. Traditional metrics used to evaluate these constructs include questionnaires, focus groups, and anonymous comment solicitations. While each of these approaches offer value, they also possess a number…

While MOOCs undoubtedly provide valuable learning resources for students, little research in the MOOC context has sought to evaluate students' learning gains in the environment. It has been long acknowledged that conversation is a significant way for students to construct knowledge and learn. However, rather than studying learning in MOOC…

Student modeling can help guide the behavior of a cognitive tutor system and provide insight to researchers on understanding how students learn. In this context, Bayesian Knowledge Tracing (BKT) is one of the most popular knowledge inference models due to its predictive accuracy, interpretability and ability to infer student knowledge. However,…

Usually a student learns to solve a system of linear equations in two ways: "substitution" and "elimination." While the two methods will of course lead to the same answer they are considered different because the thinking process is different. In this paper the author solves a system in these two ways to demonstrate the…

This paper describes how a simple application of de Moivre's theorem may be used to not only find the roots of a quadratic equation with real or generally complex coefficients but also to pinpoint their location in the Argand plane. This approach is much simpler than the comprehensive analysis presented by Bardell (2012, 2014), but it does not…

Handedness for acquiring objects was assessed monthly from 6 to 14 months in 328 infants (182 males). A group based trajectory model identified 3 latent groups with different developmental trajectories: those with an identifiable right preference (38%) or left preference (14%) and those without an identifiable preference (48%) but with a…

The analysis of variance (ANOVA) is one of the most frequently used statistical analyses in practical applications. Accordingly, the single and multiple comparison procedures are frequently applied to assess the differences among mean effects. However, the underlying assumption of homogeneous variances may not always be tenable. This study…

An inexpensive procedure for introducing the Suzuki-Miyaura coupling reaction into a high-enrollment undergraduate organic chemistry laboratory course is described. The procedure employs an aqueous palladium solution as the catalyst and a range of para-substituted aryl bromides and arylboronic acids as substrates. The coupling reactions proceed…

The Long-Term Trend (LTT) mathematics assessment of the National Assessment of Educational Progress (NAEP) used the same set of items from 1982 through 2004, including 20 items that were administered to 9-and 13-year-olds, 29 items that were administered to 13-and 17-year-olds, and 4 items that were administered at all three ages. This study used…

Accurate equating results are essential when comparing examinee scores across exam forms. Previous research indicates that equating results may not be accurate when group differences are large. This study compared the equating results of frequency estimation, chained equipercentile, item response theory (IRT) true-score, and IRT observed-score…

The process of prime factor splicing to generate home primes raises opportunity for conjecture and exploration. The notion of "home primes" is relatively new in the chronicle of mathematics. Heleen (1996-97) first described a procedure called "prime factor splicing" (PFS). The exploration of home primes is interesting and…

Given the long history of discussion of issues surrounding statistical testing and effect size indices and various attempts by the American Psychological Association and by the American Educational Research Association to encourage the reporting of effect size, most journals in education and psychology have witnessed an increase in effect size…

A central goal of the education literature is to demonstrate that specific educational interventions--instructional interventions at the student or classroom level, structural interventions at the school level, or funding interventions at the school district level, for example--have a "treatment effect" on student achievement. This paper…