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…

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…

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…

It is well known that students of inferential statistics find the hypothetical, probabilistic reasoning used in hypothesis tests difficult to understand. Consequently, they will also have difficulties in understanding "p"-values. It is not unusual for these students to hold misconceptions about "p"-values that are difficult 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…

This article reports on a classroom teaching experiment that engaged a group of high school students in designing sampling simulations within a computer microworld. The simulation-design activities aimed to foster students' abilities to conceive of contextual situations as stochastic experiments, and to engage them with the logic of hypothesis…

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…

This paper introduces a dataset and associated analysis of the scores of National Football League (NFL) games over the 2012, 2013, and first five weeks of the 2014 season. In the face of current media attention to "lopsided" scores in Thursday night games in the early part of the 2014 season, t-test results indicate no statistically…

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.)

In this paper, we discuss the importance of teaching power considerations in statistical hypothesis testing. Statistical power analysis determines the ability of a study to detect a meaningful effect size, where the effect size is the difference between the hypothesized value of the population parameter under the null hypothesis and the true value…

We compared 5 different statistics (i.e., G index, gamma, "d'", sensitivity, specificity) used in the social sciences and medical diagnosis literatures to assess calibration accuracy in order to examine the relationship among them and to explore whether one statistic provided a best fitting general measure of accuracy. College…

Our ability to statistically analyze data has grown significantly with the maturing of computer hardware and software. However, the evolution of our statistics capabilities has taken place without a corresponding evolution in the curriculum for the undergraduate chemistry major. Most faculty understands the need for a statistical educational…