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…

The product Bayes factor (PBF) synthesizes evidence for an informative hypothesis across heterogeneous replication studies. It can be used when fixed- or random effects meta-analysis fall short. For example, when effect sizes are incomparable and cannot be pooled, or when studies diverge significantly in the populations, study designs, and…

For ease of instruction in the classroom, the one-way analysis of variance F statistic is rewritten in terms of pairwise differences in individual sample means instead of differences of individual sample means from the overall sample mean. Likewise, the Kruskal-Wallis statistic may be rewritten in terms of pairwise differences in individual…

This short article continues the exploration of the Common Online Data Analysis Platform (CODAP) and statistics begun in the previous article "Statistical Investigations and CODAP, Part 1: EDA." In Part 2, the author discusses the teaching of statistical inference focusing on activities for the senior secondary years. In particular, 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…

Jokes, cartoons, songs, and games can help engage students in discussion and learning key concepts about hypothesis testing.

In the classroom, we traditionally visualize inferential concepts using static graphics or interactive apps. For example, there is a long history of using apps to visualize sampling distributions. The lineup protocol for visual inference is a recent development in statistical graphics that has created an opportunity to build student understanding.…

This article describes four semesters of introductory statistics courses that incorporate service learning and gardening into the curriculum with applications of the binomial distribution, least squares regression and hypothesis testing. The activities span multiple semesters and are iterative in nature.

Introduction: Undergraduate research experiences prepare students for graduate training or employment. Statement of problem: At many teaching-intensive universities, there is a greater demand for research experiences than there are independent study opportunities. Students from typically underrepresented backgrounds may also be unaware of a…

This article develops a set-theoretic approach to Bayes's theorem and Bayesian process tracing. In the approach, hypothesis testing is the procedure whereby one updates beliefs by narrowing the range of states of the world that are regarded as possible, thus diminishing the domain in which the actual world can reside. By explicitly connecting…

In this response, we first show that Simpson's proposed analysis answers a different and less interesting question than ours. We then justify the choice of prior for our Bayes factors calculations, but we also demonstrate that the substantive conclusions of our article are not substantially affected by varying this choice.

The number of articles showing dissatisfaction with the null hypothesis statistical testing (NHST) framework has been progressively increasing over the years. Alternatives to NHST have been proposed and the Bayesian approach seems to have achieved the highest amount of visibility. In this last part of the special issue, a few alternative…

Artificial intelligence-enabled adaptive learning systems (AI-ALS) are increasingly being deployed in education to enhance the learning needs of students. However, educational stakeholders are required by policy-makers to conduct an independent evaluation of the AI-ALS using a small sample size in a pilot study, before that AI-ALS can be approved…

Currently available (classical) testing procedures for the network autocorrelation can only be used for falsifying a precise null hypothesis of no network effect. Classical methods can be neither used for quantifying evidence for the null nor for testing multiple hypotheses simultaneously. This article presents flexible Bayes factor testing…

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…