The import or force of the result of a statistical test has long been portrayed as consistent with deductive reasoning. The simplest form of deductive argument has a first premise with conditional form, such as p[right arrow]q, which means that "if p is true, then q must be true." Given the first premise, one can either affirm or deny…

Foundations of statistics research aims to establish fundamental principles guiding inference about populations under uncertainty. It is concerned with the process of learning from observations, notions of uncertainty and induction, and satisfying inferential objectives. The growing interest in predictive methods in high-stakes fields like…

When physicians are asked to determine the positive predictive value from the a priori probability of a disease and the sensitivity and false positive rate of a medical test (Bayesian reasoning), it often comes to misjudgments with serious consequences. In daily clinical practice, however, it is not only important that doctors receive a tool with…

As a contribution to the discussion on the assessment of informal inferential reasoning (IIR) and the transition from this to formal inferential reasoning (FIR), we present a review of research on how these two types of inferential reasoning have been conceptualized and assessed. Based on our review, we discuss the need to redefine the conceptions…

Using simulation approaches when conducting randomization tests for comparing two groups in the context of experimental studies has been promoted as a beneficial approach for supporting student learning of statistical inference. Many researchers have suggested that the data production process in simulations for the randomization test intuitively…

While various studies suggest that informal statistical inference (ISI) can be developed by young students, more research is needed to translate this claim into a well-founded learning trajectory (LT). As a contribution, this paper presents the results of a cycle of design research that focuses on the design, implementation, and evaluation of the…

We present an instructional approach to teaching causal inference using Bayesian networks and "do"-Calculus, which requires less prerequisite knowledge of statistics than existing approaches and can be consistently implemented in beginner to advanced levels courses. Moreover, this approach aims to address the central question in causal…

This article examines how two processes--reasoning with statistical modelling of a real phenomenon and aggregate reasoning--can co-emerge. We focus in this case study on the emergent reasoning of two fifth graders (aged 10) involved in statistical data analysis, informal inference, and modelling activities using TinkerPlots™. We describe nine…

Although hypothesis testing is ubiquitous in data analysis, research suggests it is commonly misunderstood. Simulation-based inference methods have potential to make student thinking visible, thus providing a valuable lens to analyze developing conceptions about inference. This paper identifies difficulties made visible through simulation-based…

Teaching from an informal statistical inference perspective can address the challenge of teaching statistics in a coherent way. We argue that activities that promote model-based reasoning address two additional challenges: providing a coherent sequence of topics and promoting the application of knowledge to novel situations. We take a models and…

In the present study we analyze how students reason about or make inferences given a particular hypothesis testing problem (without having studied formal methods of statistical inference) when using Fathom. They use Fathom to create an empirical sampling distribution through computer simulation. It is found that most student´s reasoning rely on…

Currently, instruction pays little attention to the development of students' sampling variability reasoning in relation to statistical inference. In this paper, we briefly discuss the especially designed sampling variability learning experiences students aged about 15 engaged in as part of a research project. We examine assessment and…

From the perspectives of the philosophy of science and statistical inference, we discuss the challenges of making prescriptive statements in quantitative research articles. We first consider the prescriptive nature of educational research and argue that prescriptive statements are a necessity in educational research. The logic of deduction,…

In acquiring number words, children exhibit a qualitative leap in which they transition from understanding a few number words, to possessing a rich system of interrelated numerical concepts. We present a computational framework for understanding this inductive leap as the consequence of statistical inference over a sufficiently powerful…

Everyday inductive inferences are often guided by rich background knowledge. Formal models of induction should aim to incorporate this knowledge and should explain how different kinds of knowledge lead to the distinctive patterns of reasoning found in different inductive contexts. This article presents a Bayesian framework that attempts to meet…