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…

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…

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…

Recent concerns about a shortage of capacity for statistical and numerical analysis skills among social science students and researchers have prompted a range of initiatives aiming to improve teaching in this area. However, these projects have rarely re-evaluated the content of what is taught to students and have instead focussed primarily on…

A classic TV commercial once asked, "How many licks does it take to get to the center of a Tootsie Roll Tootsie Pop?" The narrator claims, "The world may never know" (Tootsie Roll 2012), but an Internet search returns a multitude of answers, some of which include rigorous systematic approaches by academics to address the…

Results from a study of 16 community college students are presented. The research question concerned how students reasoned about p-values. Students' approach to p-values in hypothesis testing was procedural. Students viewed p-values as something that one compares to alpha values in order to arrive at an answer and did not attach much meaning to…

Building on common assumptions in theories of interest and mathematics education, this experimental study examined the effect of context personalization based on individual preferences, group personalization, and example choice with preselected popular examples on middle school students' situational interest and performance in mathematics.…

Latent transition analysis (LTA) was initially developed to provide a means of measuring change in dynamic latent variables. In this article, we illustrate the use of a cognitive diagnostic model, the DINA model, as the measurement model in a LTA, thereby demonstrating a means of analyzing change in cognitive skills over time. An example is…

The statistical output of interest to most elementary statistics students is the p-value, outputted in computer programs like SPSS, Minitab and SAS. Statistical decisions are sometimes made using these values without understanding the meaning or how these values are calculated. Most elementary statistics textbooks calculates p-values for z-tests…

In introductory statistics courses, the concept of power is usually presented in the context of testing hypotheses about the population mean. We instead propose an exercise that uses a binomial probability table to introduce the idea of power in the context of testing a population proportion. (Contains 2 tables, and 2 figures.)

This study introduces a new set of weighting procedures for revealing the mediation mechanism in multi-level settings. These methods are illustrated through an investigation of whether the impact of a system-wide policy change on student outcomes is mediated by policy-induced peer composition change. When the policy changed not only…

The author describes an activity where prospective mathematics teachers made hypotheses about the dimensions of a fair cylindrical die and conducted experiments with different cylinders. He also provides a model that estimates the probability that a cylinder would land on the lateral surface, depending on the height and diameter of the cylinder.…

The authors describe a collection of dynamic interactive simulations for teaching and learning most of the important ideas and techniques of introductory statistics and probability. The modules cover such topics as randomness, simulations of probability experiments such as coin flipping, dice rolling and general binomial experiments, a simulation…

Measurement invariance in the partial credit model (PCM) can be conceptualized in several different but compatible ways. In this article the authors distinguish between three forms of measurement invariance in the PCM: step invariance, item invariance, and threshold invariance. Approaches for modeling these three forms of invariance are proposed,…