Using software to teach statistical inference in introductory courses opens the door for methods and practices that are more conceptually appealing to students. With an increasing number of fields requiring competency in statistics including data science, natural and social sciences, public health and more, it is crucial that we as instructors…

Data reasoning is an essential component of scientific reasoning, as a component of evidence evaluation. In this paper, we outline a model of scientific data reasoning that describes how data sensemaking underlies data reasoning. Data sensemaking, a relatively automatic process rooted in perceptual mechanisms that summarize large quantities of…

There is much debate about the place of probability in an introductory statistics course. While students may or may not use probability distributions in their post-collegiate lives, they will likely be faced with day-to-day decisions that require a probabilistic assessment of risk and reward. This paper describes an innovative way to teach…

The analysis of covariance (ANCOVA) is a useful statistical procedure that incorporates covariate features into the adjustment of treatment effects. The consequences of omitted prognostic covariates on the statistical inferences of ANCOVA are well documented in the literature. However, the corresponding influence on sample-size calculations for…

Too often, statistical inference and probability are treated in schools like they are unrelated. In this paper, we describe how we supported students to learn about the role of probability in making inferences with variable data by building models of real world events and using them to simulate repeated samples.

The natural experiment proposed in this article extracts three stories from boxes of "100 paper clips". The activity requires students to apply three lessons from inferential statistics, starting with a hypothesis test and including confidence intervals as well as tolerance intervals.

Survival analysis is an important analytic method in the social and medical sciences. Also known under the name time-to-event analysis, this method provides parameter estimation and model fitting commonly conducted via maximum-likelihood. Bayesian survival analysis offers multiple advantages over the frequentist approach for measurement…

In this digital ITEMS module, Dr. Roy Levy describes Bayesian approaches to psychometric modeling. He discusses how Bayesian inference is a mechanism for reasoning in a probability-modeling framework and is well-suited to core problems in educational measurement: reasoning from student performances on an assessment to make inferences about their…

Probability signifies a mainstream strand in mathematics curricula. Nonetheless, many curricular documents prepared for teachers might not offer enough support. In such a situation, a further reflection on teachers' professional knowledge for teaching probability is demanded; especially, from the perspective of probabilistic reasoning (PoPR) that…

Network meta-analysis (NMA) is gaining popularity for comparing multiple treatments in a single analysis. Generalized linear mixed models provide a unifying framework for NMA, allow us to analyze datasets with dichotomous, continuous or count endpoints, and take into account multiarm trials, potential heterogeneity between trials and network…

Probabilistic reasoning underpins much of middle school students' future work in data analysis and inferential statistics. Unfortunately for many middle school students, probabilistic reasoning is not intuitive. One specific area in which students seem to struggle is determining the probability of compound events (Moritz and Watson 2000). Research…

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…

The use of computer simulations in the teaching of introductory statistics can help undergraduate students understand difficult or abstract statistics concepts. The free software environment R is a good candidate for computer simulations since it allows users to add additional functionality by defining new functions. In this paper, we illustrate…

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…

Stan is a probabilistic programming language for specifying statistical models. A Stan program imperatively defines a log probability function over parameters conditioned on specified data and constants. As of version 2.14.0, Stan provides full Bayesian inference for continuous-variable models through Markov chain Monte Carlo methods such as the…