Online Statistics Teaching and Learning
aa r X i v : . [ s t a t . O T ] F e b Online Statistics Teaching and Learning
Jim Albert, Mine Cetinkaya-Rundel and Jingchen HuBowling Green State University, Duke University and Vassar CollegeFebruary 25, 2020
Jingchen Hu was supported by The Andrew W. Mellon Foundation Anne McNiffTatlock ’61 Endowment for Strategic Faculty Support at Vassar College and theLiberal Arts Consortium for Online Learning (LACOL).
Contents
Statistics is probably one of the most active fields to embrace and engage onlineteaching and learning. Numerous massive open online courses (MOOC) have beendeveloped and have attracted a great number of online learners. At the time ofwriting, there are 346 courses and specializations with the keyword “statistics” on2oursera , one of the most popular online learning platform. DataCamp , a growingonline learning platform specializing in data science education, has 159 courses, 22tracks, and 122 instructors. A broad survey of online statistics education is describedin [1], and a discussion of building an online statistics curriculum is contained in [2].For statistics courses at all levels, teaching and learning online poses challengesin different aspects. Particular online challenges include how to effectively and inter-actively conduct exploratory data analyses, how to incorporate statistical program-ming, how to include individual or team projects, and how to present mathematicalderivations efficiently and effectively.This chapter draws from the authors’ experience with seven different online statis-tics courses to address some of the aforementioned challenges. Section 2.1 is an onlineexploratory data analysis course taught at Bowling Green State University. Section2.2 is an upper level Bayesian statistics course taught at Vassar College and sharedamong 10 liberal arts colleges through a hybrid model. Section 2.3 is describes afive-course MOOC specialization on Coursera, offered by Duke University.All of these courses are designed for undergraduate or graduate students withcalculus backgrounds. The general aim in this chapter is to provide overviews of theseonline courses , discuss challenges and approaches, and provide general guidelines forstatistics educators interested in online teaching and learning of statistics.Yang [3] provides an overview of the components of an online statistics courseand uses student feedback to gain insight on the particular components that appeareffective for learning the statistics material. Everson and Garfield [4] discuss theuse of student discussions in an online statistics course and focus on the types ofdiscussion that appear to facilitate understanding of the statistics concepts. Dunwill[5] provides general comments about the challenges of teaching in an online formatand Everson [6] discusses her experiences in teaching online after teaching face-to-facecourses in statistics.Section 2 gives an overview of the seven online statistics courses focusing on theintended audience and the course content. Chapters 3 through 6 focus on particularcomponents of the online course, and discuss each course on how it addresses the par-ticular component. Chapter 3 discusses the problem of the online course design. Howis the instructional content presented and organized, keeping in mind the learningobjectives of the course? Chapter 4 focuses on the use of technology in each course. Astatistics course will typically include the use of some software package. What typesof software are used in each class and how is the software integrated with the learningof the conceptual material? Chapter 5 describes the different forms of assessment for For more information, visit For more information, visit datacamp.com
This online course Exploratory Data Analysis at Bowling Green State Universityfocuses on the principles of exploring data following ideas from John Tukey’s EDAbook [7]. The audience consists of graduate and undergraduate students majoringin statistics and there is a probability prerequisite.Generally, the main intent of the course is to describe an exploratory philosophyin the analysis of data. One does not wish to impose any assumptions such as normalsampling distributions or equality of variances between groups. Instead, one wishesto explore the data, looking for patterns in distributions and relationships. Thereare four “R”s in EDA that summarize the general philosophy in data exploration.“Revelation” means that EDA often uses graphical displays in data discovery. “Re-sistance” means that it is desirable to use statistical methods that are resistant ornonsensitive to outlying values. “Reexpression” means that it is sometimes useful toreexpress variables by a nonlinear transformation such as a log or square root. Last,”Residual” means that one usually wishes to look at the deviations from a statisticalfit. Table 1 shows the main units for the EDA course. The course begins with adiscussion of graphical displays and resistant summaries for a single batch of mea-surement data. The next general topic is the comparison of batches of measurementdata and the use of reexpressions to equalize spreads across batches. Properties ofthe Box-Cox power family of transformations [8] are explored in Unit 4 and thisfamily is used to perform an appropriate reexpression to make a data distributionsymmetric. Scatterplots of two measurement variables are introduced in Unit 5 andTukey’s resistant line is applied as a general method of fitting a straight line to data.In cases where the scatterplot pattern is nonlinear, a running-median smoother is de-scribed as a simple way of smoothing a scatterplot to assess the general pattern. Unit4 explores a two-way table where one summarizes a measurement variable over twocategorical variables. Median polish is a resistant method of applying an additive fit– by the use of a logarithmic transformation, this method can also be used to applya multiplicative fit to this two-way data structures. The course concludes in Unit 7by describing methods for binning measurement data, assessing if the histogram hasa Gaussian shape, and exploring batches of fraction data.Table 1: Unit and lectures for the online EDA course.Unit Lecture1. Introduction 1.1 Introduction to EDA I1.2 Introduction to EDA II2. Single Batch 2.1 Displays2.2 Summaries3. Comparing Batches 3.1 Boxplots3.2 Spread Level Plots3.3 Comparing Batches III4. Transformations 4.1 Transformations4.2 Reexpressing for Symmetry4.3 Reexpressing for Symmetry II4.4 Transformations Summary5. Plotting 5.1 Introduction to Plotting5.2 Resistant Line5.3 Plotting II5.4 Straightening5.5 Smoothing6. Two-Way Analyses 6.1 Median Polish6.2 Plotting Additive Fit6.3 Multiplicative Fit6.4 Extended Fit7. Counts and Fractions 7.1 Binning Data7.2 Binning Data II7.3 Fraction DataEDA Project 5 .2 A Bayesian Statistics Course for Cross-Campus Share
The past decades have seen great methodological, computational, and inferentialadvancement of Bayesian statistics. While Bayesian statistics continues to gain at-tention and becomes ever more popular among data analysts and researchers, thetopic itself is rarely available to students, especially at the undergraduate level. Inmost liberal arts colleges, with the staffing constraints, offering a topic course onBayesian statistics can at most be a occasional luxury. More commonly, such acourse is not offered at all.Vassar College had the chance to offer an undergraduate-level Bayesian statis-tics course in Fall 2016. The extremely positive experience with a small group ofmotivated students has encouraged the instructor to think beyond the boundary ofa physical college location. Vassar is a member of the Liberal Arts Consortium forOnline Learning (LACOL) . Under the Upper Level Math & Stats Project , startingfrom Fall 2017, the Bayesian Statistics course at Vassar College is taught locally atVassar while shared among the LACOL colleges through a hybrid model.The Upper Level Math & Stats Project focuses on sharing upper level mathemat-ics and statistics courses among participating campuses, to supplement existing andprobably limited offering while maintain the liberal arts flavor. Vassar’s BayesianStatistics course in Fall 2017 is one of the 3 courses in the pilot study (other two areupper level mathematics courses offered by two other member colleges).The student audience consists of junior and senior students. The prerequisiteincludes multivariate calculus, linear algebra, and probability. The textbook is AFirst Course in Bayesian Statistics Methods by Peter D. Hoff [9], a book mainly usedat the graduate level. The instructor intentionally borrows more applied materialfrom Bayesian Cognitive Modeling: A Practical Course, written by Michael D. Leeand Eric-Jan Wagenmakers [10], making the course more accessible to undergraduatestudents. Occasionally, advanced material from Bayesian Data Analysis by AndrewGelman and others [11] is used to supplement.There are three general sections of the course: inference, computation, and appli-cations, with main topics in each section listed in Table 2. Through the introductionof one-parameter models such as beta-binomial and normal-normal, the inference sec-tion covers the inferential basics. Moving to multi-parameter models such as normalwith two unknown parameters, computation techniques are covered. Students are LACOL is a partnership of 10 liberal arts colleges in the United States, founded in 2014. Byleveraging the power of consortial relationships, LACOL focuses on utilizing and adapting emergingtechnologies to promote excellent and innovative teaching, learning, and research in the liberal arts.For more information about LACOL, visit http://lacol.net/about-the-consortium/ For more information, visit http://lacol.net/category/collaborations/projects/upper-level-math/
Statistics with R is a specialization offered on Coursera ( )comprised of five massive open online courses (MOOCs) designed and sequenced tohelp learners master foundations of data analysis and statistical inference and mod-eling. The specialization also has a significant hands on computing component. Thetarget audience is learners with no background in statistics or computing.7he first four courses in the specialization are Introduction to Probability andData, Inferential Statistics, Linear Regression and Modeling, and Bayesian Statis-tics. These courses cover exploratory data analysis, study design, light probability,frequentist and Bayesian statistical inference, and modeling. A major focus of all ofthese courses is hands on data analysis in R; each course features computing labsin R where learners create reproducible data analysis reports as well as fully repro-ducible data analysis projects demonstrating mastery of the learning goals of each ofthe courses. The fifth course is a capstone, where learners complete a data analysisproject that answers a specific scientific/business question using a large and complexdataset. This course is an opportunity for learners to practice what they learned inthe first four courses in the specialization.Table 3 shows the modules and associated topics for each of the first four coursesin this specialization. Each subsequent course assumes learners have either completedthe previous course(s) or have background knowledge equivalent to what is coveredin them. Each module is designed to be completed in one week, though learners havethe flexibility to extend this if they need to.8 ourse 1: Introduction to Probability and Data
Data basics, observational studies and experiments, sampling and sources of bias, experimental design
Visualizing data, measures of center and spread, robust statistics, transformations, exploring bi/multivariate relation-ships, introduction to inference via simulation
Independent and disjoint events, conditional probability, Bayes’ rule, introduction to Bayesian inference
Normal and binomial distributions, assessing normality
Exploratory data analysis of data from the Behavioral Risk Factor Surveillance System
Course 2: Inferential statistics
Sampling variability and Central Limit Theorem, confidence intervals for a mean, accuracy vs. precision
Hypothesis testing for a mean, decision errors, statistical vs. practical significance t-distribution, inference for a mean and for comparing two or more means, multiple comparisons, bootstrapping
Sampling variability and CLT for proportions, confidence intervals and hypothesis tests for two or more proportions,randomization tests for small samples
Inference on data from the Behavioral Risk Factor Surveillance System
Course 3: Linear regression and modeling
Correlation, residuals, least squares line, prediction and extrapolation
Outliers. inference for regression, variability partitioning
Multiple predictors, adjusted R , collinearity and parsimony, inference for MLR, model selection and diagnostics EDA and single and multiple regression for movies data
Course 4: Bayesian statistics
Conditional probabilities and Bayes’ rule, diagnostic testing, bayes updating, Bayesian vs. frequentist definitions andinference, effect size and significance
From discrete to continuous, elicitation, conjugacy, Gamma-Poisson and Normal-Normal conjugate families, non-conjugate priors, credible intervals, predictive inference
Loss functions, minimizing expected loss, Monte-Carlo sampling, prior choice and reference priors, MCMC
Bayesian simple and multiple regression, model uncertainty and averaging, decisions under model uncertainty
Interviews with statisticians on how they use Bayesian statistics in their work
Bayesian inference and regression for movies data
Course 5: Statistics with R Capstone
Table 3: Modules and topics for the first four courses in the Statistics with R specialization ourse 1, Introduction to Data, introduces sampling and exploring data, as wellas basic probability theory and Bayes’ rule. In this course learners examine varioussampling methods, and discuss how such methods can impact the scope of inference.In addition, a variety of exploratory data analysis techniques are covered, includingusing data visualization and summary statistics to explore relationships between twoor more variables. Another key learning goal for this course is the use of statisticalcomputing, with R, for hands on data analysis. The concepts and techniques intro-duced in this course serve as building blocks for the inference and modeling coursesin the specialization.Course 2, Inferential Statistics, introduces commonly used statistical inferencemethods for numerical and categorical data. Learners learn how to set up and per-form hypothesis tests and construct confidence intervals, interpret p-values and con-fidence bounds, and communicate these results correctly, effectively, and in contextwithout relying on statistical jargon. Building on computing skills they acquired inthe previous course, learners conduct these analyses in R.In Course 3, Linear Regression and Modeling, introduces simple and multiplelinear regression. Learners learn the fundamental theory behind linear regressionand, through data examples, learn to fit, examine, and utilize regression models toexamine relationships between multiple variables. Model fitting and assessment isdone in R, and substantial amount of examples are focused on interpretation anddiagnostics for model checking.These first three courses were originally offered as a single, much longer, MOOC,for two years, before being split into shorter courses to be bundled up in a special-ization. Course 4, Bayesian Statistics, was added to the sequence at this point, inorder to make this introductory specialization more complete by adding a differentpoint of view for approaching statistical analysis.Course 4, Bayesian Statistics, introduces learners to the underlying theory andperspective of the Bayesian paradigm and shows end-to-end Bayesian analyses thatmove from framing the question to building models to eliciting prior probabilities toimplementing in R. The course also introduces credible regions, Bayesian comparisonsof means and proportions, Bayesian regression and inference using multiple models,and discussion of Bayesian prediction.The last course in the specialization is a capstone course. The materials pro-vided for this course are designed to serve as a reminder of learning goals of earliercourses or expand on them ever so slightly. A large and complex dataset is providedto the learners and the analysis requires the application of a variety of methodsand techniques introduced in the previous courses, including exploratory data anal-ysis through data visualization and numerical summaries, statistical inference, and10odeling as well as interpretations of these results in the context of the data andthe research question. Learners are encouraged to implement both frequentist andBayesian techniques and discuss in context of the data how these two approaches aresimilar and different, and what these differences mean for conclusions that can bedrawn from the data. This course was originally taught face-to-face in the classroom where the instructorwould introduce and demonstrate the EDA methods in class and the students wouldwork on weekly data analysis assignments. The online course was designed to followthe same format as the face-to-face version.1. The lecture material for the class is posted online as pdf documents. Studentshave had difficulties understanding the material by reading directly from [7]and so the lecture material seems to be a reasonable substitute for the bookmaterial. The core EDA material is contained in a series of 23 pdf documents.A particular “lecture” motivates and describes the particular EDA methodwith an illustration using the R programming language.2. There are weekly data analysis assignments and no written exams in the course.It is well-known that exams can be challenging to administer in an on-lineformat.3. The work on the assignments is a blend of statistical work such as tables andgraphs and interpretation of the results. These assignments are turned in onlineby the use of R Markdown documents saved in html format.4. All of the R code in the lecture notes is made available to the students by acollection of R scripts.
Regular face-to-face lectures are delivered in the classroom with students present atVassar College. Every lecture is broadcast and recorded by Zoom, a video conferenc-11ng software . Remote students can join the lecture in real time by a Zoom meetingID. Otherwise, they can watch the recorded videos after the videos are posted on thesame day of the lecture. This hybrid model has made lectures available in video form. With the flexibility ofmaking videos and the added familiarity of learning through videos on the students’end, some other course material has also been turned into video form. These materialhas conventionally been available as a word or pdf document.For example, when an example is not fully developed during lecture due to timeconstraint, a short video on this example is created and made available to students toreview if necessary. As another example, when many students are having problemswith the same homework question (based on observation from office hour visits),a short video on providing hint on this homework question is created and madeavailable.R programming demonstrations are very suited in video form. By watching avideo with step-by-step demonstration of programming, students are able to pausewhen needed, see things in action, and practice along the way. Several R program-ming videos are created for students in this course.
Each module includes 7-10 videos roughly 4-7 minutes in length. Most of these videosintroduce new concepts and the remaining provide additional examples and workedout problems. The slides that serve as the background in the videos are createdin Keynote (Apple’s presentation software application) and feature a substantialamount of animations such that text, visualizations, and calculations showed onthe slides follow the pace of speech in the videos. Many learners have expressed intheir course feedback that these features make the videos more engaging and easier tofollow compared to videos in many other MOOCs. Sample videos from the InferentialStatistics course are hosted on YouTube ( bit.ly/2LrO6KZ ). For more information about Zoom, visit https://zoom.us/ .3.2 Learning objectives Each module also features a set of learning objectives. A sampling of learning ob-jectives from the Inferential Statistics course are shown below: - Explain how the hypothesis testing framework resembles a court trial.- Recognize that in hypothesis testing we evaluate two competing claims: thenull hypothesis, which represents a skeptical perspective or the status quo, andthe alternative hypothesis, which represents an alternative under considerationand is often represented by a range of possible parameter values.- Define a p-value as the conditional probability of obtaining a sample statisticat least as extreme as the one observed given that the null hypothesis is true:p-value = P(observed or more extreme sample statistic | H true) These learning objectives are constructed using verbs from the revised Bloom’sTaxonomy [12] and aim to keep learners organized and focused while watching thevideos. The learners are recommended to have the learning objectives handy whilewatching the videos and revisit sections of the videos and/or suggested readings forany learning objectives that they feel like they have not mastered at the end of themodule.The learning objectives are provided as separate stand-alone documents, andafter each batch of related learning objectives are a few simple conceptual questionsfor learners to check their understanding before moving on.
Suggested readings for the first three courses come from OpenIntro Statistics [13].This book is free and open source, meaning that learners enrolled in the MOOCdo not need to additionally purchase a textbook. The readings are optional as thevideos explicitly introduce and cover all required topics for the course, however manylearners have reported in their feedback that they really like having a reference bookthat closely follows the course material. Practice problems are also suggested fromthe end of chapter exercises in this book.For the fourth course on Bayesian statistics, readings are suggested from AnIntroduction to Bayesian Thinking [14]. This textbook has been written by theBayesian Statistics course development team (faculty and PhD students) specificallyas a companion to this course and is also freely available on the web.13
Use of Technology
A special R package
LearnEDAfunctions was written for the class. This packagecontains all of the datasets used in the lecture notes and the assignments. In addition,the package contains special functions for implementing the EDA computations.For example, the function rline computes Tukey’s resistant line and the function fit.gaussian fits a Gaussian comparison curve to histogram data and outputs therootogram residuals from the Gaussian fit.
Different methods have been used to provide weekly communications with the stu-dents. For several iterations of the course, the instructor posted weekly articles on theblog “Exploratory Data Analysis” ( https://exploredata.wordpress.com/ ). In atypical post, the instructor would give an example of the weekly EDA concept andgive advice on some common problems in applying the interpreting the EDA method.Blog postings from previous years are made available for the student who wishes tosee additional illustrations of the statistical methods. Since some students expressedpreference for learning by watching videos instead of reading notes, the instructoradded some videos at the youtube channel .A particular video would show the implementation of a particular EDA method usingR and the L earnBayesfunctions package. In addition to the weekly data analysis assignments, this class also contains severalactivities where the student uses sliders and other interactive tools in exploring data.For example, in choosing the “correct” power of a reexpression, the student canchoose a value of the power on a slider and see the immediate impact of that particularreexpression in a graph of the reexpressed data.14 .2 Bayesian Course
Instead of writing on the chalkboard or presenting lecture slides on the projector infront of the classroom using a computer, the instructor uses an iPad as a participantof the Zoom meeting, bring up lecture slides inside the Zoom software, share screento present the slides to the class on the projector, and uses an Apple pencil towrite on the slide or a whiteboard. When doing R programming demonstration, theinstructor joins the Zoom meeting with a laptop, then share screen of R/RStudioon the laptop to the projector. Zoom records the video from the projector, and allaudio from the lecture. Sometimes, the instructor could use a directional mic on theiPad to improve sound capturing.
This course extensively uses videos to deliver content. One of the most creative uses ofmaking videos for this hybrid course is to create guest lectures. Conventionally, guestlectures are delivered in the physical classroom. Now, to include remote students,guest lectures can be created in video form and made available to students online.This practice also saves class meeting time when possible. For example, a guestlecture video by a cognitive science professor at Vassar College is created and usedas an introduction to Bayesian hierarchical modeling. Students watch the guestlecture before the class meeting, familiarize with the topic by themselves outside ofthe class, then when meeting in class, the lecture and discussion can follow fromthe common ground of the material from the guest lecture directly. This practicealso exposes students to applications of Bayesian statistics at various stages of theirlearning.
Each module in the course features a computing lab in R. The objective of the labsis to give learners hands on experience with data analysis using modern statisticalsoftware, R, as well as provide them with tools that they will need to complete thedata analysis projects successfully.The statistical content of the labs match the learning objectives of the respectivemodules they appear in and the application examples (i.e. datasets and researchquestions) are primarily from social and life sciences. The labs also make heavy useof an R package, statsr , which was designed specifically as a companion for the15pecialization [15]. Two other important aspects of the labs are that (1) they use the tidyverse syntax and (2) they are completed as reproducible R Markdown reports.The tidyverse is an opinionated collection of R packages designed for data science,meaning that the grammar used in the packages is optimized for working with data– specifically for wrangling, cleaning, visualizing, and modeling data [16]. The choicefor the tidyverse syntax for beginners is rooted in wanting to get learners exploringreal and interesting data and build informative and appealing visualizations anddraw useful conclusions as much as possible [17].R Markdown provides an easy-to-use authoring framework for combining statis-tical computing and written analysis in one document [18]. It builds on the ideaof literate programming , which emphasizes the use of detailed comments embeddedin code to explain exactly what the code was doing [19]. The primary benefit ofR Markdown is that it restores the logical connection between statistical comput-ing and statistical analysis by synchronizing these two parts in a single reproduciblereport. From an instructional perspective this approach has many advantages: re-ports produced using R Markdown present the code and the output in one placemaking it easier for learners to learn R and locate the cause of an error and learnerskeep their code organized and workspace clean, which is difficult for new learnersto achieve if primarily using their R console to run code [20]. Each lab is providedto the learners in an R Markdown template that they can use as a starting pointfor their lab report. Earlier labs in the specialization include lots of scaffolding, andalmost have a fill-in-the-blanks feel to them. As the course progresses the scaffoldingin the templates are removed, and by the end of the first course learners are able toproduce a fully reproducible data analysis project that is much more extensive thanany of their labs. All labs in the specialization are hosted in a publicly availableGitHub repository at https://github.com/StatsWithR/labs . In a typical data analysis assignment, the student works on a particular EDA methodusing a specific dataset or another suitable dataset chosen by the student. Onechallenge for the student is to find a suitable data structure to implement the EDAmethod. For example, if the EDA task is to symmetrize a dataset by the use ofa power expression, the student needs to find a strongly skewed dataset that could16enefit with a reexpression.
In a final capstone project, the students selects his or her own dataset, states somequestions of interest, and explores the dataset using several of the EDA methodsdiscussed in class. The focus of this project is not on the implementation of themethods but rather in the interpretation of the results in light of the questions thatwere originally posed.
Homework is on a biweekly basis. The assignment usually consists of a set of deriva-tion exercises to enhance the understanding of Bayesian methodology, and a set ofapplication-based exercises, which requires the uses of R programming. There aretwo midterm exams and no final exam.The teaching assistant for this course holds regular office hours at Vassar. Whilethese office hours are held online too, remote students rarely make use of them.Instead, the instructor meets with the remote students together during a separatelyscheduled online office hour, also through Zoom.Homework submission from the remote students is done through scans and emails.Exams for remote students are proctored by the local faculty liaison. Exam papersare sent to the instructor by scans and emails too. All grading is either done by theinstructor or the teaching assistant. Graded homework and exams are returned tothe remote students by scans and emails.
Towards the latter part of the semester, when students have been exposed and gainedsome experience with Bayesian inference, students are grouped to do case studies withreal data applications. These case studies are all open-ended. Students are given thechance to freely explore the datasets and come up with their methods and realizetheir inferences through MCMC computation techniques.Prior to the case study class meeting, groups need to post their analyses onto theMoodle discussion forum to receive credit. Students in the same group take turn tobe the leading writer of the analyses. Such practice ensures that everyone is prepared17o discuss the approaches and findings from the group, and the class meetings usuallyturn out to be great discussion sessions and ideas bounce back and forth.
As mentioned before, the course has a final project component, and students canchoose from one of the following.- A Bayesian data analysis on a topic of your choosing.- A new Bayesian methodology or theoretical finding.- A Bayesian research paper or a book chapter (choose from a provided list).Students submit project proposal after the first midterm exam. They are encour-aged to meet with the instructor to discuss their project ideas and their progressalong the way.The final project presentation has two parts: a 2-min video on Moodle, anda poster at the poster session. The choice of a poster session is to accommodate arelatively large class (16 local students). However, it mimics real research settings, asit has become common for academic conferences to have a poster session for graduatestudents and junior researchers. Students in the class overall enjoy being able to talkto audience as a small group. The amount of interaction between presenters and theaudience is much more than a regular presentation.
Each module also features two sets of multiple choice quizzes, one formative and onesummative. Each question is encoded with feedback that points learners back torelevant learning objectives. Learners can attempt the summative quizzes multipletimes with slightly modified versions of the questions.
Each course ends with a data analysis project, the focus of which is summarized inTable 3, and the specialization wraps up with an extended capstone project. Eachstudent who turns in a project evaluates three other students’ work using a peerevaluation rubric. Learners are also strongly encouraged to seek informal feedback on18heir projects in the course discussion forums. All data analysis projects appearing inthe courses in this specialization are hosted in a publicly available GitHub repositoryat https://github.com/StatsWithR/projects . Currently, there is limited interaction in this course. Students communicate withthe instructor by means of personal meetings or email or messages sent through thelearning management system. There is no regularly planned interaction betweenstudents such as an outline chat session, But students are asked to read and reviewthe project presentations of two other students in the class.
To create and foster an online learning community, there are extensive uses of theonline discussion forum on Moodle .At the beginning of the semester, students make self-introduction posts abouttheir basic information (name, year, and school), prior statistics exposure, prior Rexposure and potential final project interests.During the semester, online discussion forums are created whenever sharing ofinformation and making comments are needed, and they are for credit sometimes.For example, when covering the Gibbs sampler, the class reads a research paperExplaining the Gibbs Sampler by George Casella and Edward I. George [21]. Areading guide for this paper with 6 questions is provided to the students. Priorto the class meeting, students need to respond to any one question on the onlinediscussion forum to receive participating credit. After the class discussion, studentsneed to make another response for receive credit. Such requirement not only helpsstudents in reading a statistics research paper outside of class, but also helps facilitateboth in-class discussion by more engagement prior and post class meeting.There is a final project for students in the course. In addition to present theirprojects in a poster session at the end of the semester, students need to make a2-min video post about their projects on the online discussion forum. Watching a2-min pitch talk prior to the poster session helps other students to arrange their Moodle is the course management system used at Vassar College.
Student interaction, or the lack thereof of in person interaction, is often a majorchallenge in online courses. However in MOOCs the discussion forums are often amajor strength of the course. Given that at any point thousands of students areenrolled in the course, even if a small percentage of these students choose to browsethe discussion forums, and an even smaller percentage of them interact with otherlearners on the course discussion forums, this still results in a large number of learnersinteracting with each other.Additionally, over the years of the MOOC being offered, a handful of very knowl-edgeable and helpful course mentors emerged from the discussion forums. These arelearners who took the courses at some point and now volunteer their time to answerstudent questions and provide direction for new learners.
There are several current challenges in the current version of the EDA online course. • Interaction with the studentIt is beneficial if the student can interact with the instructor and fellow studentsin an online course. Some attempts for interaction such as online chat sessionsor online message boards don’t appear to be effective in this particular class.So most of the communication is done through email and personal meetings.There is an effort to try out new methods of interaction when they becomeavailable. • Technology issuesStudents can get frustrated with technology issues such as installing softwareor getting their R markdown files to “knit” properly. It is best to address these20ssues early in the course so the course is more about the EDA concepts andless about the associated technology. • Balance of computation and interpretation in assignment workIn a typical assignment, the student will turn in a Markdown file that blendsoutput from the R system and written text that interprets the R output in thecontext of the particular applied problem. Since the course is really focusingon the interpretation rather than the implementation of the EDA methods, theassignment should emphasize the interpretation component. Depending on thebackground, the student may emphasize instead the computation component,but hopefully the students will learn what is expected in future assignments.
Although the instructor has been faced with various challenges, advice, suggestions,and sharing from multiple parties have been tremendously helpful. To improve theteaching and learning mode of the hybrid model, lecture videos can be edited andshortened when resources permit. If done properly, the lecture videos can well be a setof learning material for anyone (not necessarily from the LACOL member colleges)who is interested in an undergraduate-level introduction to Bayesian statistics. Morethought and consideration on turning course material into video form can furtherenhance the teaching and learning. While students’ interaction can be maintainedusing online discussion forum on Moodle, other forms of interaction can be exploredand developed to further enhance the overall interaction in the course.
There are three main challenges with offering this content on an online platform; twoof these are associated with to the labs and the other is associated with the dataanalysis projects. • Autograding: Given that this is a course with thousands of learners enrolledat any given point, human-grading is simply not feasible. The lab assessmentsare set up as multiple choice questions. Learners complete the lab exercises bygenerating R Markdown reports in which they analyze a dataset. Then, theyanswer a series of multiple choice questions about the data analysis results. Thechallenge is that the multiple choice questions do not assess the full spectrumof the skills we want learners’ to acquire via these labs – they assess whether21hey can obtain the correct results using R, however they do not assess masteryof R syntax, reproducibility of their analysis, etc. • Computing infrastructure: Our preferred method for getting students with nocomputing background started with R is a cloud-based access to RStudio inorder to avoid challenges around local installation and to provide a uniformcomputing environment for all learners. However it is not feasible to offer acentralized cloud-based solution to all learners enrolled in a MOOC, and hencestudents have to locally install R and RStudio and the correct versions of allpackages they use in the labs.As a partial solution for this challenge, we offer students the option to completethe labs in the first course of the specialization on DataCamp ( ),an online learning platform that provides in-browser access to RStudio. Thishelps students struggling with software installation issues early on in the courseto get started with data analysis and go back to tackling software challengesonce they feel a little bit more confident with R. • Peer evaluation: Autograding is not feasible for open ended data analysisprojects, and hence peer evaluation is the only solution for grading of theseprojects. Even with a very detailed rubric, consistency in grading is difficultto attain, and it is challenging for learners who are just learning the materialthemselves to evaluate others’ work. Additionally, variability in quality anddepth of feedback provided leaves can leave learners frustrated. The option toshare their projects on the discussion forums and get feedback can be helpfulfor some learners, but others are not so keen on publicly sharing their projects.
Although these is current interest in teaching online introductory statistics courses,the online statistics courses described here are directed towards specific groups ofstudents and all of the comments may not be directly applicable to the introductoryclass. For example, the students in the EDA online course are primarily masters-levelor advanced undergraduate students who are comfortable in working independentlyon assignments and projects, and this particular course design may not be suitablefor an introductory statistics class with a minimal mathematics prerequisite. Butthere are general common elements to these courses which would be helpful for theinstructor who is designing the first online statistics course.22 resentation of Content
Although there is some written instructional content in the EDA course, there isan extensive use of videos in all of these online courses. The use of videos makesit possible for several instructors to get involved in the presentation of content. Inaddition, it is possible for the student to learn from the video at his or her own pace,replaying parts of the video to help understand the material.
Interaction
It is important to develop a cooperative learning environment among students in theonline course. These courses suggest some useful methods for facilitating this typeof environment. Discussion forums, as described by the Five-Course MOOC, are onegood way to foster communication between students. Another good opportunity forcollaboration is through statistics projects where groups of students explore data oncase studies.
Assessment
It should be noted that traditional forms of assessment such as multiple choice examsplay a limited role in assessment for these online statistics courses. Instead, thesecourses feature data analysis projects, interactive computer lab assignments, andother projects where the student does an exploration into a new method or findingthat is not covered in the curriculum.
Using Software
All of these online courses use technology or software that may not familiar to thestudent. Specifically, since these are statistics courses, one would typically use theR software together with some specialized R packages. Introducing this technologycreates some challenges since the students can vary greatly with their experience withthe R system. These courses have presented some ways to mitigate these technologychallenges by creating special packages (such as the LearnEDA package in the EDAcourse) that include all of the datasets and special functions needed for the course.The Five-Course MOOC provides some suggestions to help some of these technologyissues such as using a cloud-based version of the R system or outsourcing some ofthe tutorial R material to a company such as DataCamp. The instructor teachingan online statistics course should think carefully about the use of software, especiallyfrom the viewpoint of the student who is inexperienced with technology.23 eferences [1] J. D. Mills and D. Raju, “Teaching statistics online: A decade’s review of theliterature about what works,”
Journal of Statistics Education , vol. 19, no. 2,2011.[2] D. S. Young, G. F. Johnson, M. Chow, and J. L. Rosenberger, “The challengesin developing an online applied statistics program: Lessons learned at penn stateuniversity,”
The American Statistician , vol. 69, no. 3, pp. 213–220, 2015.[3] D. Yang, “Instructional strategies and course design for teaching statistics on-line: perspectives from online students,”
International Journal of STEM Edu-cation , vol. 4, no. 34, pp. 1–15, 2017.[4] M. Everson and J. Garfield, “An innovative approach to teaching online statisticscourses,”
Technology Innovations in Statistics Education , vol. 2, no. 1, 2008.[5] E. Dunwill, “Teaching principles transferred to online courses: strategies to use,” eLearning Best Practices , 2016.[6] M. Everson, “10 things i learned about teaching online,” eLearn Magazine , 2009.[7] J. W. Tukey,
Exploratory Data Analysis . Pearson, 1977.[8] R. M. Sakia, “The box-cox transformation technique: a review,”
The Statisti-cian , pp. 169–178, 1992.[9] P. D. Hoff,
A First Course in Bayesian Statistical Methods . Springer Texts inStatistics, Springer-Verlag New York, 2009.[10] M. D. Lee and E. Wagenmakers,
Bayesian Cognitive Modeling: A PracticalCourse . Cambridge University Press, 2014.[11] A. Gelman, J. B. Carlin, H. S. Stern, D. B. Dunson, A. Ve-htari, and D. B.Rubin,
Bayesian Data Analysis . Chapman & Hall/CRC Texts in StatisticalScience, 3rd ed., 2013.[12] L. W. Anderson, D. R. Krathwohl, P. W. Airasian, K. A. Cruikshank, R. E.Mayer, P. R. Pintrich, J. Raths, and M. C. Wittrock, “A taxonomy for learning,teaching, and assessing: A revision of blooms taxonomy of educational objec-tives, abridged edition,”
White Plains, NY: Longman , 2001.2413] D. M. Diez, C. D. Barr, and M. C¸ etinkaya Rundel,
OpenIntro Statistics . Cre-ateSpace, 3rd ed., 2014. .[14] M. Clyde, M. C¸ etinkaya Rundel, C. Rundel, D. Banks, C. Chai, andL. Huang,
An Introduction to Bayesian Thinking . GitHub, 1st ed., 2018. https://statswithr.github.io/book/ .[15] C. Rundel, M. Cetinkaya-Rundel, M. Clyde, and D. Banks, statsr: CompanionPackage for Statistics with R , 2018. R package version 0.1-0.[16] H. Wickham, tidyverse: Easily Install and Load the ’Tidyverse’ , 2017. R packageversion 1.2.1.[17] D. Robinson, “Teach the tidyverse to beginners.” http://varianceexplained.org/r/teach-tidyverse/ , 2017.[18] Y. Xie, J. Allaire, and G. Grolemund,
R Markdown: The Definitive Guide . CRCPress, 2018.[19] D. E. Knuth, “Literate programming,”
The Computer Journal , vol. 27, no. 2,pp. 97–111, 1984.[20] M. C¸ etinkaya-Rundel and C. Rundel, “Infrastructure and tools for teachingcomputing throughout the statistical curriculum,”
The American Statistician ,vol. 72, no. 1, pp. 58–65, 2018.[21] G. Casella and E. I. George, “Explaining the gibbs sampler,”