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…

The multi-faceted nature of mathematics knowledge for teaching, including pedagogical content knowledge (PCK), has been studied widely in elementary classrooms, but little research has focused on senior secondary mathematics teaching. This study utilised the Knowledge Quartet (Rowland et al., "Research in Mathematics Education," 17(2),…

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 article presents a case study that explores digital experiences in statistics teaching within Danish lower secondary school, focusing on the development of students' statistical concepts. The study tracks the progress of a student named Frida, who engages with the digital tool TinkerPlots over the span of a year. Frida developed a unique…

We examined the performance of coefficient alpha and its potential competitors (ordinal alpha, omega total, Revelle's omega total [omega RT], omega hierarchical [omega h], greatest lower bound [GLB], and coefficient "H") with continuous and discrete data having different types of non-normality. Results showed the estimation bias was…

Several international large-scale assessments were conducted at the turn of the new century, and during the past two decades the Programme for International Student Assessment (PISA) completed seven cycles of assessment to facilitate practitioners' policy debates and governance. This study reviews PISA-related articles published in English and…

Recently Burkholder "et al." argued that class normalized gains over the entire population of courses is approximated by a Cauchy distribution, not by a normal distribution, and therefore should not be used to compare different classes because means and standard deviations cannot be calculated. They argued that multiple linear regression…

Sampling distributions are fundamental for statistical inference, yet their abstract nature poses challenges for students. This research investigates the development of high school students' conceptions of sampling distribution through informal significance tests with the aid of digital technology. The study focuses on how technological tools…

The negative hypergeometric distribution is often not formally studied in secondary or collegiate statistics in contexts other than drawing cards without replacement. We present a different context with the potential of engaging students in simulating and exploring data.

In this paper, we address the following questions: What misconceptions do high school students exhibit in their first encounter with significance test problems through a repeated sampling approach? Which theory or framework could explain the presence and features of such patterns? With brief prior instruction on the use of Fathom software to…

Multiple group modeling is one of the methods to address the measurement noninvariance issue. Traditional studies on multiple group modeling have mainly focused on item responses. In computer-based assessments, joint modeling of response times and action counts with item responses helps estimate the latent speed and action levels in addition to…

When students with the capacity to succeed in a 4-year college do not take a college admission test, this represents a potential loss of opportunity for students and colleges alike. However, the costs of testing--both pecuniary and nonpecuniary--may exceed the benefits for students who lack the interest in or qualifications for college attendance.…

Recent standards reform documents across the globe have called for statistical literacy by the end of high school. Thus, it is important for teachers to develop a deep understanding of the content. Despite the relatively thick literature base connecting students' content knowledge and reasoning, research on these connections among practicing…

Informally testing the fit of a probability distribution model is educationally a desirable precursor to formal methods for senior secondary school students. Limited research on how to teach such an informal approach, lack of statistically sound criteria to enable drawing of conclusions, as well as New Zealand assessment requirements led to this…