Binary logistic regression is one of the most widely used statistical tools. The method uses odds, log odds, and odds ratios, which are difficult to understand and interpret. Understanding of logistic regression tends to fall down in one of three ways: (1) Many students and researchers come to believe that an odds ratio translates directly into…

Common sense is a dynamic concept and it is natural that our (statistical) common sense lags behind the development of statistical science. What is not so easy to understand is why common sense lags behind as much as it does. We conduct a survey among Japanese students and provide examples and tentative explanations of a number of statistical…

Two novel proofs show that the sum of a specific pair of normal random variables is not normal are established in this note. This is one of the most often misunderstood facts by first-year students in probability theory and statistics. The first proof is concise using the moment generating function. The second proof checks whether the moments of…

Humans implicitly pick up on probabilities of stimuli and events, yet it remains unclear how statistical learning builds expectations that affect perception. Across 29 experiments, we examine the influence of task-irrelevant distributions--defined across acoustic frequency--on both tone detection in noise and tone duration judgments. The shape and…

It is increasingly recognised that to be informed citizens and to participate fully in the workforce requires an understanding of statistical data and risk. Such understanding is underpinned by statistical reasoning. It has been shown, however, that students have difficulty moving from concrete representations and procedural mathematical…

The objective of this article is to discuss the development of statistical and probabilistic reasoning in childhood as a result of an interdisciplinary project, involving the fields of mathematics, statistics, and life sciences. This is a case study with three 10-year-old students from a Brazilian school. The children's oral and written narratives…

Aotearoa New Zealand is a super diverse nation in terms of the ethnicities of its people and languages spoken. With an increased rate of immigration from various parts of the world, the presence of multiple languages in many domains of social life is a reality. Consequently, classrooms are now places where learners have different linguistic and…

Solving real-life problems through mathematical modeling is one of the aims of modern mathematics curricula. For this reason, prospective mathematics teachers need to acquire modeling skills and use these skills in learning environments in terms of creating rich learning environments. With this study, it is aimed to examine the reflections of…

In recent years, converging evidence has suggested that prediction plays a role in language comprehension, as it appears to do in information processing in a range of cognitive domains. Much of the evidence for this comes from the N400, a neural index of the processing of meaningful stimuli which has been argued to index the extent to which a word…

This paper reports the statistical and probabilistic reasoning of young children in terms of randomness, variability, and data representations in the context of informal inferential reasoning (IIR). Using the IIR approach, a task was designed and conducted one-on-one with 28 children aged 5 to 6 years old, in a case study setting. The researcher…

A commonly-held belief is that many university students are 'assessment-driven'; that is, students engage more with activities that are assessed compared with those that are not. 'Incentivised engagement' includes the practice of providing incentives (such as marks or otherwise) for students to engage in particular activities. Perusall is a social…

Sequence learning is fundamental to a wide range of cognitive functions. Explaining how sequences--and the relations between the elements they comprise--are learned is a fundamental challenge to cognitive science. However, although hundreds of articles addressing this question are published each year, the actual learning mechanisms involved in the…

This study investigates a range of non-normative ideas that pre-service teachers (PSTs) employ in reasoning about sampling variability. This issue was studied in the context of a content course on statistics and probability for pre-service middle grade teachers at a Midwestern American university. Analysis of seven PSTs' video and screen records…

This research presents the results of the implementation of a model-eliciting activity called Brickyards, designed to promote the learning of the binomial distribution. The theoretical framework used was the Models and Modeling Perspective, and the participants were undergraduate students enrolled in a probability and statistics course of the…

Students studying statistics often misunderstand what statistics represent. Some of the most well-known misunderstandings of statistics revolve around null hypothesis significance testing. One pervasive misunderstanding is that the calculated p-value represents the probability that the null hypothesis is true, and that if p < 0.05, there is…