Topic 4 : Statistics education at the post-secondary levelThe discipline of statistics is itself changing in response to vast supplies of data, technological and theoretical advances to tackle more and more complex real problems, and the ready access to powerful open source and commercial software. Students leave post-secondary institutions for a rapidly changing workplace. Statistics graduates need to be prepared for a world of data mining, resampling, Bayesian inference, nonparametric smoothing, computer-intensive techniques, and multivariate contexts. Graduates in other disciplines need to be prepared for workplaces and projects increasingly dependent on statistics and the growing body of statistical methodologies and techniques. All these swirling currents of change and challenge demand a creative revision and reshaping of our curricula and our modes of delivery. We need sustainable approaches that address the reality that Statistics education is vulnerable to backsliding, reductionism and a multiplicity of miscellaneous pressures both intentional and inadvertent.
Session 4A: Randomisation and bootstrapping: the quick way to inference
4A1: Accepting the challenge: constructing a randomisation pathway for inference into our traditional introductory courseA Marie Fitch University of Auckland, New Zealand
Matt Regan University of Auckland, New Zealand
Current thinking in the statistical education community is that a randomisation pathway, with the aid of dynamic visualisations, will provide students with a more accessible and better conceptual understanding of the thinking underpinning statistical inference than a traditional normality-based approach. We report on where we are currently at in introducing randomisation methods into our large introductory course. Continuous reflection on our construction of this pathway has been and will continue to be an important part of working out its implementation. We include an outline of some principles we have tried to adhere to, issues we have encountered, and the main constraints by which we have been bound.
4A2: Using simulation/randomization to introduce p-value in week 1Soma Roy California Polytechnic State University, United States
Nathan Tintle Dordt College, United States
Jill VanderStoep Hope College, United States
Todd Swanson Hope College, United States
Allan Rossman California Polytechnic State University, United States
George Cobb Mount Holyoke College, United States
Beth Chance California Polytechnic State University, United States
In traditional introductory Statistics courses, statistical inference is often not introduced until the last third of the course, leaving little time for students to develop a strong understanding of the meaning of a p-value. We use simulation and randomization methods to introduce statistical inference early in our introductory Statistics courses, which allows us to discuss concepts of statistical investigations, significance, and p-value in week 1. We start with one-proportion examples to build on students’ intuition about “Is the observed result surprising, if both outcomes are equally likely?” Having established the core concept of the logic of inference, we repeat the cycle for situations involving one mean, two proportions, and so on, to contexts involving several proportions, several means, and two quantitative variables. Here we describe the implementation of this approach by showing examples of our student activities, and demonstrating our use of applets to bolster student understanding and learning.
4A3: Intuitive introduction to the important ideas of inferenceRobin Lock St. Lawrence University, United States
Dennis Lock Iowa State University, United States
Eric Lock Duke University, United States
Patti Frazer Lock St. Lawrence University, United States
Kari Lock Morgan Duke University, United States
Concepts of statistical inference, such as margin of error when estimating a parameter and p-value when testing a hypothesis, are notoriously difficult for students to grasp. In traditional approaches, these ideas typically come as the culmination of a long development of prerequisite material on sampling distributions, formulas for standard errors, standard reference distributions, central limit theorems, and formulas for standardizing values. Simulation methods, such as bootstrap intervals and randomization tests, require minimal background knowledge and highlight the underlying logic of statistical inference, giving students an intuitive appreciation for the key ideas early in a course. But are such methods accessible and understandable to beginning students? We argue that advances in technology make this approach both feasible and desirable. So how does one go about modifying a course to incorporate these ideas? That question is the main focus of this paper.
Session 4B: Use of student response systems in teaching statistics at the university level
4B1: Clickers, simulations, and conceptual understanding of statistical inferenceJennifer Kaplan University of Georgia, United States
This paper is a technology case study that addresses the theme of using clicker technology in a large lecture format undergraduate introduction to statistics class to develop student conceptual understanding of inference. The paper will present one of a suite of activities designed to help students develop conceptual understanding inference. The activity, targeting understanding of the process of hypothesis testing and the meaning of the p-value, has been implemented in a large lecture introductory statistics course in which the students use calculators to perform a trial of a simulation and clickers to report the results of the trial. Design features of the activity along with slides and student responses will be shared. An extension of the activity designed to improve student understanding of Type I and II errors and power as well as classroom implementation issues and future directions for research will be discussed.
4B2: Teaching data analysis in large classes using clicker assessmentMichael Forster University of Auckland, New Zealand
A search of the statistical education literature on “engagement”, “active learning” and similar terms yields multiple papers. A common thread of these papers is getting students involved in the “process of statistics” by getting them to design observational studies, experiments and survey instruments, and to collect data in class, to bring to class or for use in small-group projects. The idea underlying these activities appears to be that if students are involved in the process of statistics they will better learn and understand the subject. Since 2011, I have been experimenting with clickers in large second and third year classes in data analysis. When clickers are used for in-class assessment, I have found that attendance, performance, enjoyment and student evaluations all show positive improvements. In this paper I look at some qualitative and quantitative results of various clicker models.
4B3: Teaching discrete distributions using contingent teaching with clickersWayne Stewart University of Oklahoma, United States
Sepideh Stewart University of Oklahoma, United States
In most undergraduate statistics courses students are introduced to discrete random variables which are later accompanied by a list of probability functions and examples of their applications. The students are required to determine from a story problem what discrete probability distribution is appropriate. This process involves appreciating the defining characteristics of the distributions and distilling from the problem those characteristics that enable the learner to decide on the correct distribution. This initial classification which is an important first step in solving the problem must be accompanied by more guidance on how to proceed. This study will describe a teaching routine which uses contingent teaching in conjunction with clicker provided feedback from students to enhance students’ categorization strategies.
4B4: Personal response systems as a learning aid in an epidemiology course for postgraduate statistics studentsGillian Lancaster Lancaster University, United Kingdom
Andrew Titman Lancaster University, United Kingdom
Personal response systems (PRS), also known as ‘clickers’, are most commonly used in large introductory lectures for undergraduate students to anonymously send responses to questions posed by the lecturer. We consider the use of PRS in a masters course setting where groups are typically smaller but where statistics students may be reluctant to participate interactively in lectures for fear of admitting they do not understand the problem, or even that they do understand. We use PRS at intermittent places throughout the Principles of Epidemiology module to check students’ understanding and knowledge of the topic using a variety of multiple choice questions within each lecture. Module design, choice and evaluation of questions, wait and response times and student feedback will all be discussed.
Session 4C: Rank-based inference, association measures and nonparametric statistics
4C1: Is the real world normal?Catherine Dehon Free University of Brussels, Belgium
In recent times, we have become increasingly confronted with high dimensional data sets. Statistical methods have had to adapt themselves to more complex questions from many different scientific disciplines, notably in the social sciences. But in spite of this evolution, statistics courses still rely too often on artificial examples that contribute to the myth that the real world is quite simple. Classical statistics based on parametric models also feature in undergraduate and graduate curricula. Nevertheless apparent deviations of the model cannot always be ignored. For example, we often expect large datasets to contain a small number of unusual observations, which renders classical procedures unreliable. The theory of robust statistics deals with small deviations from the model, and can be viewed as a compromise between parametric and nonparametric analysis. Should we consider introducing these modern concepts into undergraduate statistics courses?
4C3: Combining nonparametric inferences using data depth, bootstrap and confidence distributionDungang Liu Yale University, United States
Min-ge Xie Rutgers University, United States
Regina Y Liu Yale University, United States
For the purpose of combining inferences from several nonparametric studies for a common hypothesis, we develop a new methodology using the concepts of data depth and confidence distribution (CD). In recent years, the concept of CD has attracted renewed interest and has shown high potential to be an effective tool in statistical inference. In this project, we use the concept of CD, coupled with data depth, to develop a new approach for combining the test results from several independent studies for a common multivariate nonparametric hypothesis. Specifically, in each study, we apply data depth and bootstraps to obtain a p-value function for the common hypothesis. The p-value functions are then combined under the framework of combining confidence distributions. The method will be illustrated using simulations and aircraft landing performance data.
4C4: Should we still teach rank-based distribution-free procedures?E Jacquelin Dietz Meredith College, Raleigh, United States
For decades, I have enjoyed teaching rank-based distribution-free inference procedures for two distinct reasons. First, I have believed these are useful data analysis methods that should be part of any applied statistician’s repertoire of statistical methods. Second, I have found rank-based tests ideal for teaching hypothesis testing – many students report that they never really understood sampling distributions and p-values until they studied rank-based tests. Recently, many instructors have begun teaching inference in introductory courses using bootstrapping and randomization tests in place of traditional normal theory methods. New software has made it feasible to apply randomization methods to the original observations. Is there now less motivation to rank data? Can we teach the fundamental concepts of hypothesis testing just as well using randomization methods on the original observations? Are rank procedures still important methods of data analysis that we should be teaching to our students?
Session 4D: Exchanging pedagogy between post-secondary and secondary school statistics courses
4D1: Exchanging statistics pedagogy between the master teacher and the future teacherDeborah Nolan University of California at Berkeley, United States
Cal Teach is a science and math teacher preparation program modeled after UTeach at the University of Texas, Austin. Math for America (MfA), Berkeley, which is part of the national MfA effort, is a 5-year master teacher fellowship program for experienced math and science teachers. Both programs aim to prepare K-12 teachers to excel by strengthening their pedagogical content knowledge and their science content knowledge. We describe the role that statistics education plays in these two synergistic programs and make recommendations how aspects of these efforts might be more broadly adopted.
4D2: Statistics for all studentsCourtney Couvreur Oakland International High School, United States
How can statistics instructors — at the high school and college level — make the development of statistical thinking and 21st century skills accessible to all students? Alongside the rise of Big Data, the ability to reason statistically will appreciate; all students need a strong introductory statistics course to prepare them for the statistical demands they will encounter in higher education, work, and engaged citizenship. The traditional high school coursework neglects statistics for all but advanced students. With the Common Core State Standards for Mathematics, there is an opportunity to infuse statistical thinking into each grade level for all K-8 students, followed by a choice of statistics courses (Advanced Placement or non-AP) in high school. To take advantage of this opportunity, all math teachers must be adequately trained in statistics. Furthermore, secondary and post-secondary educators must work together meet the demands that will be placed on all of our students.
4D3: Exchanging pedagogy between post-secondary and secondary school statistics coursesKim Gilbert University of Georgia, Athens, United States
Can we expect the high school graduate of 2020 to be a better “statistical thinker” than those who are graduating today? Possibly, if the new Common Core State Standards (CCSS) for mathematics are successfully implemented. What impact will these CCSS have on the Advanced Placement high school course and on the traditional introductory college course? Ideas, including randomization/simulation-based methods, about what may happen will be presented.
4D4: Exchanging pedagogy between post-secondary and secondary school statistics courses: facilitating meaningful professional developmentJosh Tabor Canyon del Oro High School, United States
With the implementation of the Common Core State Standards in the United States, all teachers of mathematics in grades 6–12 will also be teachers of statistics. College faculty should play an important role in developing the statistical content knowledge of these teachers, as well as teachers of AP Statistics. Successful examples of professional development for K–12 teachers will be highlighted and future opportunities will be discussed.
Session 4E: We know you need to know statistics, do you?
4E1: Measuring university students’ approaches to learning statistics: a cross-cultural and multilingual version of the ASSISTCaterina Primi University of Florence, Italy
Maria Virginia Lopez University of Buenos Aires, Argentina
Maria del Carmen Fabrizio University of Buenos Aires, Argentina
Francesca Chiesi University of Florence, Italy
Ayse Bilgin Macquarie University, Australia
University students often encounter difficulties in statistics courses that hinder their progress in the attainment of their degree. In identifying variables that may constitute barriers faced by students, it is important to investigate the approach that students adopt in learning statistics. Focusing on issue of measurement, the present paper aimed to develop a brief version of the Approaches and Study Skills Inventory for Students (ASSIST), one of the well-known measures of a student’s approach to learning. The final goal was to obtain a cross-cultural and multilingual version of the ASSIST to investigate learning approaches in multinational research. Results indicated that the abbreviated Spanish, Italian and English versions of the ASSIST showed good psychometric properties and the three-factor structure of the original version (Deep, Surface and Strategic approaches) was confirmed.
4E2: A comparison of attitudes between traditional and hands-on classes in an introductory statistics courseCarl Lee Central Michigan University, United States
Aklilu Zeleke Michigan State University, United States
Kundana Divi Central Michigan University, United States
Jennifer Daniels Central Michigan University, United States
Chin-I Cheng Central Michigan University, United States
In this paper we present a comparison study of students’ attitudes toward statistics. We administered attitude surveys to three sections of an introductory statistics course. Two of these sections were small classes, taught by a “traditional” lecture based format. The third section was a large class, taught using a “hands-on” active-learning approach. The surveys collected responses on factors such as Learning Styles, Affect, Cognitive Competence, Value and Difficulty. The survey responses were used to compare students’ attitude towards statistics between the two class formats.
4E3: Turkish ASSIST: measuring university students’ approaches to learning statisticsAyse Bilgin Macquarie University, Australia
Sitki Gozlu Faculty of Engineering, Turkey
Evidence-based decision making has become one of the most valuable tools for any profession with the ease of accessing vast amounts of data due to developments in computing and data storage facilities. This is especially important for future generations in management positions. Undoubtedly statistics play an important role in enabling managers to base their decisions on valid available evidence, but if students do not acquire the skills to understand and evaluate them during courses in statistics, their ability to utilise this evidence may be limited. In this study we investigated the learning approaches of students in statistics who are studying towards a management science or management engineering degree in six Turkish universities using Turkish Approaches and Study Skills Inventory for Students (TASSIST) which is translated from English to Turkish. This paper presents an exploratory factor analysis for the validation of Turkish ASSIST.
Session 4F: Opening up the data world wider and faster
4F1: Introductory statistics in the 21st centuryRichard De Veaux Williams College, United States
Big data is everywhere. Companies, governments and the media can’t seem to get enough of the data deluge and the tsunami of data that is about to overwhelm us and/or make us a smarter planet. But, what’s the connection between the Statistics taught in an introductory statistics course and the statistical analyses that are performed throughout the world every day? How close is this version of Statistics to real world practice?
Most courses in Statistics now start with exploratory data analysis, move on to probability and then inference. If time permits, they include models, often ending at simple regression. Unfortunately, models are the most important topic, and comprise the core of modern big data analytics. Maybe we’re teaching the course backward. We’ll describe an approach that starts the course with models, making full use of students’ intuition about the world and exposing them early to the power of statistical models
4F2: DataFest: celebrating data in the data delugeRobert Gould University of California, Los Angeles, United States
DataFest is an undergraduate competition in which student teams have just 48 hours to find and communicate meaning in a rich, complex data set. Many of the skills and practices of data science—working collaboratively with a team, organizing raw data, dealing with non-traditional data types, sorting through datasets with hundreds of variables—are hard to teach in a classroom setting. Assigning projects is one approach, but in our experience, many student projects were far below the level we hoped that students would achieve. DataFest, which now includes participants from fifteen U.S. colleges and universities, provides an opportunity for students to challenge themselves with realistic, large data sets in an intense, fun, and encouraging environment.
4F3: Middleware for Middle EarthChris Wild University of Auckland, New Zealand
With the “data deluge”, “big data”, “data science” and a growing emphasis on the importance of analytics it no longer makes sense to stay with our historical curriculum. It is all far too slow and conveys far too little of what the data world has to offer. We have to find ways to get students much further into the world of data, much faster. This must of necessity involve jettisoning significant parts of what we currently do and replacing them by more “valuable” alternatives. Charting a way forward involves identifying values, followed by goals, then priorities and then strategies. We flesh out these issues and convey some visualisation-based glimpses of possible futures. We propose a class of software specifically aimed at allowing learners to experience extracting stories from a wide range of data types rapidly and steal the computer-science term middleware to name it.
4F4: Open data, civil society and monitoring progress: challenges for statistics educationJoachim Engel Ludwigsburg University of Education, Germany
The paper discusses the role of statistical knowledge for active participation in democratic processes. It is based on the assumptions that knowledge and skills to reason adequately with data are an important prerequisite for the functioning of democracy in our mass societies. While open data nowadays are easily accessible through National Statistics Organizations, UN offices and NGOs like Gapminder etc., statistics educators face the challenge to teach quantitative skills needed to understand and interpret these data. Drawing information from very big multivariate data sets may involve statistical principles different from dealing with small samples. Besides strengthening the civil society, integrating issues of monitoring social progress lets students experience that statistical analyses play a role in understanding the pressing social and political issues of our time.