Most current statistics courses include some instruction relevant to causal inference. Whether this instruction is incorporated as material on randomized experiments or as an interpretation of associations measured by correlation or regression coefficients, the way in which this material is presented may have important implications for…

Recent research suggests the benefits of supporting a progressive understanding of concepts of inference prior to the teaching of procedures and formal calculations through the study of informal statistical inference (ISI). To contribute to the growing knowledge about the early learning and teaching of statistics, particularly regarding the…

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…

Data modeling is an essential activity in a data-driven society, but such a topic and how the context shapes it has received limited attention. This paper reports on research that investigated the role of context in supporting early statistical reasoning in the data modeling process. The data were collected throughout sessions in which young…

This paper reports on a study concerning the social nature of young students' informal inferential reasoning. Employing inferentialism as a background theory, we examine cognitive and sociocultural aspects of reasoning that arose during group discussions as well as trace relations between those aspects. Following a design experiment approach, we…

The study reported in this article investigated the appropriateness of Mathematical Knowledge in Teaching of three pre-service primary school teachers (PSTs), teaching an informal statistical inference (ISI) lesson to primary school students. Using an ISI framework and the Knowledge Quartet framework, the presence and appropriateness of the PSTs'…

In statistical inference, importance of sampling is recognized as one of its key concepts, which has allowed its incorporation internationally in different curricular guidelines and specifically in the Chilean curriculum, since the first notions of sampling are introduced in 7th Grade. This paper presents an analysis of the responses to an…

Using simulation-based inference (SBI), such as randomization tests, as the primary vehicle for introducing students to the logic and scope of statistical inference has been advocated with the potential of improving student understanding of statistical inference and the statistical investigative process. Moving beyond the individual class…

This study examines informal hypothesis testing in the context of drawing inferences of underlying probability distributions. Through a small-scale teaching experiment of three lessons, the study explores how fifth-grade students distinguish a non-uniform probability distribution from uniform probability distributions in a data-rich learning…

The purpose of this study was to develop the Basic Literacy In Statistics (BLIS) assessment for students in an introductory statistics course, at the postsecondary level, that includes, to some extent, simulation-based methods. The definition of statistical literacy used in the development of the assessment was the ability to read, understand, and…

In their response to our paper, Nicholson and Ridgway agree with the majority of what we wrote. They echo our concerns about the misuse of inferential statistics and NHST in particular. Very little of their response explicitly challenges the points we made but where it does their defence of the use of inferential techniques does not stand up to…

White and Gorard make important and relevant criticisms of some of the methods commonly used in social science research, but go further by criticising the logical basis for inferential statistical tests. This paper comments briefly on matters we broadly agree on with them and more fully on matters where we disagree. We agree that too little…

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…

Grade 6 (modal age 11) students invented and revised models of the variability generated as each measured the perimeter of a table in their classroom. To construct models, students represented variability as a linear composite of true measure (signal) and multiple sources of random error. Students revised models by developing sampling…

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…