Over the last decade, there has been a 10-fold increase in the number of published systematic reviews of prevalence. In meta-analyses of prevalence, the summary estimate represents an average prevalence from included studies. This estimate is truly informative only if there is no substantial heterogeneity among the different contexts being pooled.…

Many students persistently misinterpret histograms. Literature suggests that having students solve dotplot items may prepare for interpreting histograms, as interpreting dotplots can help students realize that the statistical variable is presented on the horizontal axis. In this study, we explore a special case of this suggestion, namely, how…

Multivariate count data is ubiquitous in many areas of research including the physical, biological, and social sciences. These data are traditionally modeled with the Dirichlet Multinomial distribution (DM). A new, more flexible Dirichlet-Tree Multinomial (DTM) model is gaining in popularity. Here, we consider Bayesian DTM regression models. Our…

As reporting of effect sizes in evaluation studies has proliferated, researchers and consumers of research need tools for interpreting or benchmarking the magnitude of those effect sizes that are relevant to the intervention, target population, and outcome measure being considered. Similarly, researchers planning education studies with social and…

The ability to interpret and compare data distributions is an important educational goal. Inherent in the statistical concept of distribution is the need to focus not only on individual data points or small groups of data points (so-called local view), but to perceive a distribution as a whole, allowing to recognize global features such as center,…

Many students persistently misinterpret histograms. This calls for closer inspection of students' strategies when interpreting histograms and case-value plots (which look similar but are different). Using students' gaze data, we ask: "How and how well do upper secondary pre-university school students estimate and compare arithmetic means of…

This is the fourth in a series of statistical articles for mathematics teachers. In this article, the authors discuss topics in General Mathematics in Unit 2 Topic 1 (Univariate data analysis and the statistical investigation process) and topics in Essential Mathematics, Unit 2 Topic 1 (Representing and comparing data).

BASIE is a framework for interpreting impact estimates from evaluations. It is an alternative to null hypothesis significance testing. This guide walks researchers through the key steps of applying BASIE, including selecting prior evidence, reporting impact estimates, interpreting impact estimates, and conducting sensitivity analyses. The guide…

A distinction is made between scores as measures of a construct and predictions of a criterion or outcome variable. The interpretation attached to predictions of criteria, such as job performance or college grade point average (GPA), differs from that attached to scores that are measures of a construct, such as reading proficiency or knowledge…

Data transformations have been promoted as a popular and easy-to-implement remedy to address the assumption of normally distributed errors (in the population) in linear regression. However, the application of data transformations introduces non-ignorable complexities which should be fully appreciated before their implementation. This paper adds to…

This thesis examined middle school students' current understanding of variability using a constructed response item assessment question. Variability is an essential concept in the teaching and learning of statistics. However, many students have difficulty with the concept of variability especially when constructing boxplots. Using a framework…

Box plots are frequently misinterpreted and educational attempts to correct these misinterpretations have not been successful. In this study, we used two instructional techniques that seemed powerful to change the misinterpretation of the area of the box in box plots, both separately and in combination, leading to three experimental conditions,…

Research has shown that forest plots are a gold standard in the visualization of meta-analytic results. However, research on the general interpretation of forest plots and the role of researchers' meta-analysis experience and field of study is still unavailable. Additionally, the traditional display of effect sizes, confidence intervals, and…

Recent studies have shown that the interpretation of graphs is not always easy for students. In order to reason properly about distributions of data, however, one needs to be able to interpret graphical representations of these distributions correctly. In this study, we used Tversky's principles for the design of graphs to explain how 125…

There is no comprehensive database of U.S. district-level test scores that is comparable across states. We describe and evaluate a method for constructing such a database. First, we estimate linear, reliability-adjusted linking transformations from state test score scales to the scale of the National Assessment of Educational Progress (NAEP). We…