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An International Journal on the Teaching and Learning of
Statistics
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JSE Volume 22, Number
2 Abstracts
Engaging students in active learning can enhance their understanding and appreciation of a subject such as statistics. Classroom activities and projects help to engage students and further promote the learning process. In this paper, an activity investigating the influence of population size and wealth on the medal counts from the 2012 London Olympics is suggested, and the relevant data is provided.
Key Words: Least squares; Linear models; Regression.
New Zealand has been leading the world in terms of the data handling, and in more recent years, data visualisation approach in its school statistics curriculum. In 2013, bootstrapping and randomisation were added to the senior secondary school (Ministry of Education 2012). This paper gives an historical perspective of the people and groups that have influenced this statistical literacy based curriculum, including the local professional statisticians’ association, the New Zealand Statistical Association (NZSA). The paper includes a short analysis of factors contributing to the successful implementation of the curriculum and its possible long-term impact on tertiary statistics teaching. It also outlines the impact of some of these New Zealanders, such as Professors David Vere-Jones and Chris Wild, and also Maxine Pfannkuch and John Harraway, on statistics education internationally through their involvement in the International Association for Statistical Education (IASE) and their statistics education research activities.
Key Words: Statistics education; Statistics education research; Statistics education in New Zealand; School statistics curricula; History of the International Association for Statistical Education.
In this article, I introduce a novel applet (“module”) for exploring probability distributions, their samples, and various related statistical concepts. The module is primarily designed to be used by the instructor in the introductory course, but it can be used far beyond it as well. It is a free, cross-platform, stand-alone interactive application based on Wolfram Research’s novel computable document format (CDF) technology. It features over thirty common discrete and continuous distributions and can be used to illustrate concepts such as random samples, population and sample means and medians, histograms, kernel density estimators, boxplots, and cumulative distribution, survival, and hazard functions all while dynamically linking samples and estimators to adjustable distribution parameters in real-time. Additionally, the module includes real-world datasets to aid in communicating the concept of fitting a distribution to data. It is hoped that the module will be helpful to instructors at both the high school and college levels for the conceptual understanding of distributions. A simplified version geared specifically toward out-of-class student learning in the introductory course is also made available for students’ use. Both are accessible from http://www.baylor.edu/statistics/disttool.
Key Words: Probability distributions; Wolfram CDF technology; Interactive learning environments; Monte-Carlo simulation.
Histograms are adept at revealing the distribution of data values, especially the shape of the distribution and any outlier values. They are included in introductory statistics texts, research methods texts, and in the popular press, yet students often have difficulty interpreting the information conveyed by a histogram. This research identifies and discusses four misconceptions prevalent in student understanding of histograms. In addition, it presents pre- and post-test results on an instrument designed to measure the extent to which the misconceptions persist after instruction. The results presented indicate not only that the misconceptions are commonly held by students prior to instruction, but also that they persist after instruction. Future directions for teaching and research are considered.
Key Words: Histograms; Introductory Statistics; Undergraduate Student Learning; Misconceptions.
This paper provides a statistical investigation of the impact of heart rate levels on training effect for a specific exercise regimen, including an analysis of post-exercise heart rate recovery. Results indicate optimum target values for both average and maximum heart rate during exercise in order to improve both cardiorespiratory and cardiovascular fitness levels. The statistical methods used in the analysis are typically covered in college level Statistics I & II courses, and various classroom implementation strategies are presented.
Key Words: Post exercise heart rate recovery; Multiple regression; Interaction model;
Matched-sample hypothesis testing.
Correlated predictors in regression models are a fact of life in applied social science research. The extent to which they are correlated will influence the estimates and statistics associated with the other variables they are modeled along with. These effects, for example, may include enhanced regression coefficients for the other variables—a situation that may suggest the presence of a suppressor variable. This paper examines the history, definitions, and design implications and interpretations when variables are tested as suppressors versus when variables are found that act as suppressors. Longitudinal course evaluation data from a single study illustrate three different approaches to studying potential suppressors and the different results and interpretations they lead to.
Key Words: Suppressors; Suppression effects; Multicollinearity; Course evaluations; Student ratings of instruction.
The “law of large numbers” indicates that as sample size increases, sample statistics become less variable and more closely estimate their corresponding population parameters. Different research studies investigating how people consider sample size when evaluating the reliability of a sample statistic have found a wide range of responses, from no consideration of sample size to over consideration of sample size. This paper provides a qualitative meta-analysis of
studies that have used what we dub the “Hospital Task” for investigating peoples’ thinking
about the role of sample size in parameter estimation. This paper aims to investigate what the Hospital Task can tell us about how people make decisions under uncertainty and the usefulness of the task for developing models of students’ statistical reasoning. To achieve these goals, we review the original task, synthesize results of other studies which have used some version of this task, provide a critique of the different versions of the task, discuss implications of the task for research, and provide insights and viewpoints from a small group of statisticians. The paper concludes with implications for further research.
Key Words: Sample size; Variability; The law of large numbers; Statistical reasoning; Sampling distributions.
Richard L. Scheaffer and Tim Jacobbe
The purpose of this paper is to provide a brief history of statistics in the K-12 setting in the United States. This is intended to serve as a reminder of how far the discipline has come in its inclusion in the standard curriculum for all students as well as to highlight the need for research in this area.
Key Words: K-12; Curriculum; Students; Teachers.
Shaun S. Wulff and Timothy J. Robinson
Bayesian methodology continues to be widely used in statistical applications. As a result, it is increasingly important to introduce students to Bayesian thinking at early stages in their mathematics and statistics education. While many students in upper level probability courses can recite the differences in the Frequentist and Bayesian inferential paradigms, these students often struggle using Bayesian methods when conducting data analysis. Specifically, students tend to struggle translating subjective belief to the specification of a prior distribution and the incorporation of uncertainty in the Bayesian inferential approach. The purpose of this paper is to present a hands-on activity involving the Beta-Binomial model to facilitate an intuitive
understanding of the Bayesian approach through subjective problem formulation which lies at the heart of Bayesian statistics.
Key Words: Beta-Binomial; Conjugate prior; Prior specification; Subjective probability.
Interviews
with Statistics Educators
Jessica Utts is Professor and Chair of Statistics at the University of California – Irvine. She is a Fellow of the American Statistical Association and a recipient of a Founders Award from ASA. She has been elected as President of ASA for the year 2016. This interview took place via email on February 13 – May 18, 2014.
Teaching
Bits
I located 15 articles that have been published from March through June 2014 that pertained to statistics education. In this column, I highlight a few of these articles that represent a variety of different journals that include statistics education in their focus. I also provide information about the journals and book and a link to their websites so that abstracts of additional articles may be accessed and viewed.
The aim of this short column is to provide an overview of resources and events from CAUSEweb (www.causeweb.org) and MERLOT (www.merlot.org) to help you stay connected with the Statistical Education community.
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