Measuring one physical quantity as a function of another often requires making some choices prior to the measurement process. Two of these choices are: the data range where measurements should focus and the number (n) of data points to acquire in the chosen data range. Here, we consider data range as the interval of variation of the independent…

Recall of remembered locations reliably reflects a compromise between a target's true position and its region's prototypical position. The effect is quite robust, and a standard interpretation for these data is that the metric and categorical codings blend in a Bayesian combinatory fashion. However, there has been no direct experimental evidence…

Competence data from low-stakes educational large-scale assessment studies allow for evaluating relationships between competencies and other variables. The impact of item-level nonresponse has not been investigated with regard to statistics that determine the size of these relationships (e.g., correlations, regression coefficients). Classical…

In an informal study, two versions of a story involving probability are introduced to undergraduates. The findings reveal that students have troubles detecting equal probabilities in a sampling scheme without replacement in which no information on earlier draws is available.

College binge drinking has been linked to student stress. Which among a variety of stressors are more likely to result in problem drinking? In this paper, the relative influence of three types of stressors on college binge drinking is considered, including the academic, interpersonal, and developmental (e.g., making decisions about the future,…

Typically, in education and psychology research, the investigator collects data and subsequently performs descriptive and inferential statistics. For example, a researcher might compute group means and use the null hypothesis significance testing procedure to draw conclusions about the populations from which the groups were drawn. We propose an…

This article introduces a Bayesian method for testing the axioms of additive conjoint measurement. The method is based on an importance sampling algorithm that performs likelihood-free, approximate Bayesian inference using a synthetic likelihood to overcome the analytical intractability of this testing problem. This new method improves upon…

The ability to effective learn, process, and retain new information is critical to the success of any student. Since mathematics are becoming increasingly more important in our educational systems, it is imperative that we devise an efficient system to measure these types of information recall. "Assessing and Measuring Statistics Cognition in…

Single-case design is a repeated-measures research approach for the study of the effect of an intervention, and its importance is increasingly being recognized in education and psychology. We propose a Bayesian approach for estimating intervention effects in SCD. A Bayesian inference does not rely on large sample theories and thus is particularly…

Value-added models are being implemented in many states in an attempt to measure the contributions of individual teachers and schools toward students' learning. Scores from these models are increasingly used for high-stakes purposes such as setting compensation, hiring or dismissing teachers, awarding tenure, and closing schools. The statistician…

The Rail Trail and Property Values dataset includes information on a set of n = 104 homes which sold in Northampton, Massachusetts in 2007. The dataset provides house information (square footage, acreage, number of bedrooms, etc.), price estimates (from Zillow.com) at four time points, location, distance from a rail trail in the community, biking…

The purpose of this study is to examine the validity of the scale for identifying gifted children, whose validity was proven by exploratory, confirmatory factor analysis, and whose reliability was proven the Cronbach alpha coefficient for identifying children in the 3-6 age group, using Mokken scaling based on nonparametric item response theory.…

Scenario-based writing assessment has two salient characteristics by design: a lead-in/essay scaffolding structure and a unified scenario/topic throughout. In this study, we examine whether the scenario-based assessment design would impact students' essay scores compared to its alternative conditions, which intentionally broke the scaffolding…

Most studies on the relationship between students' socioeconomic status (SES) and student achievement assume that its effects are sizable and causal. A large variety of theoretical explanations have been proposed. However, the SES-achievement association may reflect, to some extent, the inter-relationships of parents' abilities, SES, children's…

Middle school mathematics teachers often do not emphasise statistics and geometry in their lesson plans for a variety of reasons. However, these are integral topics in mathematics, and using direct lecture or hands-on activities may have different effects on teacher confidence when approaching these subjects. Using qualitative and quantitative…