Adapting Statistics Instruction for an Online Environment in the Wake of COVID-19

Contributing author Christopher Engledowl is an Assistant Professor of Mathematics Education and Quantitative Research Methods at New Mexico State University.

The world is currently experiencing unprecedented forced movement from face-to-face interaction to a completely virtual form of interaction. Higher education institutions have quickly made sweeping policy decisions that have, overnight, overhauled the classroom learning environment. These decisions have resulted in many people questioning the kinds of quality that can be expected—especially from instructors who have never taught an online course Simultaneously, many organizations have expanded the capacity of their digital platforms to accommodate the insurgence of people making use of their products for teaching and learning.

For instance, Discord—an application with free voice and text chat originally designed for gamers to interact in real time with one another, read more here—recently increased the capacity for live streaming for up to 50 people for the sole purpose of making it more amenable to online instruction. They also published a blog post about how to use Discord for instructional purposes, including a special pre-organized setup to help streamline the interface for new users.

Just as many others have recently experienced, my institution has recently dictated the movement of face-to-face courses to an online setting in order to practice social distancing and follow government recommendations designed to slow the spread of COVID-19. I am currently in the process of transitioning my face-to-face courses to online format, and I am making use of Discord. In this article, I will showcase how I made use of Discord in a prior online course, what I observed about student interactions, and what students reported about their experiences. I believe Discord can be an effective, and easy to implement, tool for creating quality discourse.

Some Context: Advanced Statistics in College of Education

In the Summer of 2019, I taught a required doctoral level course for an online-only program in a College of Education called Advanced Statistics. This course is comparable to a typical undergraduate level introductory course in statistics. In the pre-requisite course, students are exposed to basic descriptive statistics and visualizations, leading up to a two-sample t-test. Advanced Statistics extends this learning to include ANOVA, ANCOVA, and simple linear regression. The student population ranges in age from 25 to 50, whose only experience with statistics is the prerequisite course, where I have had students tell me that they had never seen a boxplot before! The course is application-based and ends with a small-scale project where students explore their own research question using either their own data, or data from the 2012 PISA—which is used throughout the course.

Because it was an online course, in addition to including the kinds of instructor presence and interaction that have been discussed by John Haubrick on this blog, I also was asking myself: How do I emulate the important student-to-student interaction that would occur in a synchronous, face-to-face setting, as suggested by the Guidelines for Assessment and Instruction in Statistics Education (GAISE) College Report?

Using Discord to Promote Quality Interaction

What is Discord?

Discord is an application designed with both text and voice chat “channels” within a “server.” The server is the larger space that only invited members can interact within, and it is composed of channels where members chat. Discord text chat channels are free-flowing chat streams. This was highly appealing to me because threaded comments can have the side-effect of conversations only existing in small groups, without ever making their way into the larger classroom discussion. Moreover, because Discord has integrated tagging (using the @ symbol), it makes it easy for everyone to see who is having side conversations, while also allowing others to enter into that same conversation—thus promoting them to the whole group level.

How Can it Promote Discussion?

In the Advanced Statistics course, because the majority of students were teachers and administrators in K–12 schools, this course was managed largely asynchronously. I used Discord as the central place for managing the classroom environment. I regularly posted links to videos on my YouTube Channel and I also posted announcements for the few times I conducted livestreams using a free application called Twitch. Thus, Discord was used for nearly all student-student and student-instructor interaction. To encourage students to get to know one another more, and make discussions feel more authentic, I set up a #general chat channel for them to discuss anything they wanted to, where I would not be monitoring unless I was tagged. I also created a #current-music-jam and #current-reading-interest channel. Many students made use of these channels at different points, and I also shared my own reading and music interests.

The course-specific channels I created to align with course learning goals were #roller-coaster-tycoon (to discuss assignments related to this dataset), #spss-discussion, #research-interests, and #p-values. Channels are very easy to add at a moment’s notice, but these seem to have sufficed for the course and were meant to work toward the GAISE recommendations to “foster active learning” and to “use technology to explore concepts and analyze data” (p. 3). It also supported students as we worked toward the GAISE goals regarding the investigative process, understanding statistical models, and understanding inference (p. 6). Discord supported these goals by providing a space where students could engage in productive discourse with one another to deepen their knowledge. For instance, as can be seen in the two screenshots below, students frequently inserted screenshots of output they were trying to make sense of in order to crowd source whether their interpretations were correct. I largely stayed out of these conversations, and found that many students would enter into the conversations, resulting in dialogic interactions that everyone learned from. Sometimes these conversations would head in an unproductive direction, but because I could see the entire conversation—unlike if it was occurring outside of class or in a group discussion in a face-to-face class where it might be difficult to hear what occurred—I could point directly back to the conversation using tagging—or even just tagging @everyone—or a screenshot and help steer students in a productive direction. This cannot be overstated: Being able to see entire conversations in this way is an incredible advantage over face-to-face discussions. It allows, in a sense, an omniscient perspective—one that everyone in the entire class also enjoys the benefits of.

How Can it Improve Instruction?

On the administrative side of teaching, to encourage participation, I evaluated both the quantity and quality of contributions using a simple rubric. Searching for a student’s username produces a list of every contribution they have made, along with a timestamp and the place in the chat stream where the comment was made—faded in the background. You can also filter contributions by channel. To see the contributions in the context of where they occurred in the chat, a simple click on the background reveals them. This process was very efficient, taking about 2-3 minutes per student.

What Did Students Say About Discord?

In an anonymous poll, I asked students: How useful did you find Discord? On a scale of 1 (Not At All) to 5 (Very Useful), 54% rated it a 5 and 23% rated it a 4. No one rated it below a 3. A follow up item asked students what they liked about Discord, and many responses were things like, “it is very interactive and we’re free to ask any questions we need at any given time” and “nice interactions that you could follow.” When asked what they did not like about Discord, students described issues that would exist even if the courses were face-to-face (e.g., “I couldn’t work ahead because I had to be involved in discussions”). Other responses were simple complaints (e.g., “Another platform”).

Perhaps even more revealing were the comments students gave when asked to compare ways of interacting in the Canvas learning management platform vs. Discord. Many responses included statements such as “Discord is best for discussion in real time” or “Discord seemed easier to follow than discussions on Canvas (and I teach online using Canvas)….seems less formal and more able to operate like a texting stream.” I will leave with this last revealing comment. When discussion turns into “I’ll do it just for the grade,” we have lost a major opportunity to promote deep learning through social interaction:

Discord is best for discussion in real time. Canvas is ok, more for turning in work and such—Posting discussion board responses and getting feedback, it is more assignment based.

Hello, is anyone there? Instructor presence in an online statistics course

Contributing author John Haubrick is an instructional designer and assistant teaching professor for the Penn State Department of Statistics where he supports the teaching and design of the online statistics courses.

With the prevalence of online chat bots and robocalls, we sometimes find ourselves asking: “Are you a machine or a real person?” Students can also experience this when taking an online course with an “absent” instructor. Instructor presence in an online course has been cited in research as a major influence of student satisfaction and engagement, which may impact their ability to learn the course content (e.g., Ladyshewsky, 2013; Gray and DiLoreto, 2016). So what can we do to “show up” to class as an online statistics instructor?

The Community of Inquiry (CoI) framework (Garrison, Anderson, & Archer,  2000) is one model used to classify the types of instructor presence for a rich educational experience. The framework is based on three types of presence: Social, Teaching, and Cognitive. You can find a large collection of publications and resources related to the CoI framework on the CoI website. In the model, the entire educational experience is the result of the interrelationship (or overlap) of the social, teaching and cognitive presence. Let’s explore each presence and how they might apply to an online statistics course.

Social Presence

Social presence shows that you are a real human teaching the students. Examples of incorporating social presence in an online course include…

Start of the course

  • Post an introductory video to put your face and voice with a name. Share your interests, hobbies, research, and the keys to success in your course.
  • Use an introduction forum to allow everyone to share a thing or two about themselves. Make the prompts interesting and provide various format options. Educational social media platforms like Flipgrid and Yammer provide text, audio, and video options beyond the standard text based discussion boards.

Throughout the course

Teaching Presence

Teaching presence refers to the technical set-up and design of the learning management system and the design of the learning materials that the students engage with (e.g., content, activities, assessments). Examples of integrating Teaching Presence in an online course include…

  • Provide clear directions on how to get started the first time they enter the course.
  • Have contact information, resources, and links for finding help and support. This includes technical support, resources for statistics software, and who to contact (e.g., TAs, instructors, other) and when.
  • Create navigation through the course that is clear and optimized for efficiency.
  • Make expectations and directions clear, thorough, and concise on all learning materials.
  • Offer timely, constructive, and frequent feedback in a variety of formats (text, audio, video). Your LMS might offer built-in or integrated media tools, such as Zoom, VoiceThread, Kaltura or YouTube.  

Cognitive Presence

The cognitive presence determines how students create meaning of the course content. Through activities, assignments, and discussions, the instructor can challenge and lead students through the content. Examples of creating Cognitive Presence in an online course include…

  • Create a reflection journal where students can make their thinking visible. For example…
    • You could set up a 3-2-1 post, where they post: 3 key concepts of the lesson, 2 ways in which they can apply the concept to their life, work, or future career, and 1 challenge or difficulty they are still having.
  • Provide lesson overview videos connecting the new content to prior knowledge or previous lessons. Demonstrate how the new content fits into the big picture of the course (or program). 
  • Have students “make sense” of output from statistical software or results from a research article by asking questions about conceptual understanding rather than procedural knowledge.
  • Have students spot errors in worked examples that might include incorrect calculations, equations, software code, software output, or hypothesis testing conclusions. 

The examples provided are just a sample of the myriad of options available for creating presence in an online course. However, THE most important thing is to show up! Your presence is important. Presence can create a positive learning community that will not only motivate your learners, but you as well.



Ladyshewsky, Richard K. “Instructor Presence in Online Courses and Student Satisfaction.” International Journal for the Scholarship of Teaching and Learning, vol. 7, no. 1, Jan. 2013. (Crossref), doi:10.20429/ijsotl.2013.070113.

Garrison, D. Randy, et al. Critical Inquiry in a Text-Based Environment: Computer Conferencing in Higher Education. 1999. Semantic Scholar, doi:10.1016/S1096-7516(00)00016-6.

Gray, Julie A., and Melanie DiLoreto. “The Effects of Student Engagement, Student Satisfaction, and Perceived Learning in Online Learning Environments.” International Journal of Educational Leadership Preparation, vol. 11, no. 1, May 2016. ERIC,

Visual Inference: Using Sesame Street Logic to Introduce Key Statistical Ideas

As outlined by Cobb (2007), most introductory statistics books teach classical hypothesis tests as

  1. formulating null and alternative hypotheses, 
  2. calculating a test statistic from the observed data, 
  3. comparing the test statistic to a reference (null) distribution, and 
  4. deriving a p-value on which a conclusion is based.

This is still true for the first course, even after the 2016 GAISE guidelines were adapted to include normal- and simulation-based methods. Further, most textbooks attempt to carefully talk through the logic of hypothesis testing, perhaps showing a static example of hypothetical samples that go into the reference distribution. Applets, such as StatKey and the Rossman Chance ISI applets, take this a step further, allowing students to gradually create these simulated reference distributions in an effort to build student intuition and understanding. While these are fantastic tools, I have found that many students still struggle to understand what the purpose of a reference distribution is and the overarching logic of testing. To remedy this, I have been using visual inference to introduce statistical testing, where “plots take on the role of test statistics, and human cognition the role of statistical tests” (Buja et al., 2009). In this process, I continually encourage students to apply Sesame Street logic: which one of these is not like the other? By using this alternative approach that focuses on visual displays over numerical summaries, I have been pleased with the improvement in student understanding, so I thought I would share the idea with the community.

Visual inference via the lineup protocol

In visual inference, the lineup protocol (named after “police lineup” for criminal investigations) provides a direct analog for each step of a hypothesis test. 

  1. Competing claims: Similar to a traditional hypothesis test, a visual test begins by clearly stating the competing claims about the model/population parameters. 
  2. Test statistic: A plot displaying the raw data or fitted model (we’ll call it the observed plot) serves as the “test statistic” under the visual inference framework. This plot must be chosen to highlight features of the data that are relevant to the hypotheses in mind. For example, a scatterplot is a natural choice to examine whether or not there is a correlation between two quantitative variables, but will be less useful in the examination of association between a categorical and a quantitative variable. In that situation, side-by-side boxplots or overlaid density plots are more useful.
  3. Reference (null) distribution: Null plots are generated consistently with the null hypothesis and the set of all null plots constitutes the reference (or null) distribution. To facilitate comparison of the observed plot to the null plots, the observed plot is randomly situated in the field of null plots, just like a suspect is randomly situated amongst decoys in a police lineup. This arrangement of plots is called a lineup.
  4. Assessing evidence: If the null hypothesis is true, then we expect the observed plot to be indistinguishable from the null plots. If you (the observer) are able to identify the observed plot in the above lineup, then this provides evidence against the null hypothesis. If one wishes to calculate a visual p-value, then lineups need to be presented to a number of independent observers for evaluation. While this is possible, it is not a productive discussion in most intro stats classes that don’t do a deep dive into probability theory.    


As a first example in class, I use the creative writing experiment discussed in The Statistical Sleuth. The experiment was designed to explore whether creativity scores were impacted by the type of motivation (intrinsic or extrinsic). To evaluate this, creative writers were randomly assigned to a questionnaire where they ranked reasons they write: one questionnaire listed intrinsic motivations and the other listed extrinsic motivations. After completing the questionnaire, all subjects wrote a Haiku about laughter, which was graded for creativity by a panel of poets. Below, I will give a brief overview of each part of the visual lineup activity.

Competing claims

First, have my students discuss what competing claims are being investigated. I encourage them to write these in words before linking them with the mathematical notation they saw in the reading prior to class. The most common answer is: there is no difference in the average creative writing scores for the two groups vs. there is a difference in the average creative writing scores for the two groups. During the debrief, I make sure to link this to notation:


H_{A}:\mu_{intrinsic} - \mu_{extrinsic}\neq 0

EDA review

Next, I have students discuss what plot types would be most useful to investigate this claim, reinforcing topics from EDA.

Lineup evaluation

Most students recognize that side-by-side boxplots, faceted histograms, or density plots are reasonable choices to display the relevant aspects of the distribution of creative writing scores for each group. I then give them a lineup of side-by-side boxplots to evaluate (note I place a dot at the sample mean for each group), such as the one shown below. Here, the null plots are generated by permuting the treatment labels; thus, breaking any association present between the treatment and creativity scores. (I don’t give the students these details yet, I just tell them that one plot is the observed data while the other 19 agree with the null hypothesis.) I ask the students to

  1. choose which plot is the most different from the others, and
  2. explain why they chose that plot.

[Your turn! Try it out yourself! Which one of these is not like the other?]

Lineup discussion

Once all of the groups have evaluated their lineups and discussed their reasoning, we regroup for a class discussion. During this discussion, I reveal that the real data are shown in plot 10, and display these data on a slide so that we can point to particular features of the plot as necessary. After revealing the real data, I have students return to their groups to discuss whether they chose the real data, and whether their choices support either of the competing claims. Once the class regroups and thoughts are shared, I make sure that the class realizes that an identification of the raw data provides evidence against the null hypothesis (though I always hope students will be the ones saying this!).

Biased observers

When I first started this activity, I showed the students the real data prior to the lineup, which made them biased observers. Consequently, students had an easier time choosing the real data, and the initial discussion within their groups wasn’t as rich. However, I have seen little impact on the follow-up discussion focusing on whether the data are identifiably different and what that implies. 

Benefits of the lineup protocol

The strong parallels between visual inference and classical hypothesis testing make it a natural way to introduce the idea of statistical significance without getting bogged down in the minutiae/controversy of p-values, or the technical issues of describing a simulation procedure before students understand why that’s important. All of my students understand the question “which one of these is not like the others,” and this common understanding has generated fruitful discussion about the underlying inferential thought process without the need for a slew of definitions. In addition, after this activity I find it easier to discuss how we generate permutation resamples and conduct permutation tests, because students have seen permutations in lineups and have already thought about evaluating evidence.

Where would this fit into your course?

As you’ve seen, I use the lineup protocol in my intro stats course to introduce the logic behind hypothesis tests. 

In addition, I use visual inference to help students build intuition about new and unfamiliar plot types, such as Q-Q plots, mosaic plots, and residual plots. For example, when I introduce students to mosaic plots using the flying data set in the fivethirtyeight R package, I pick one pair of categorical variables, such as one’s opinion on whether it’s rude to bring a baby on a plane and their self-identified gender. Then, I have students create the mosaic plot and discuss what they see. Once they have recorded their thoughts, I provide a lineup consisting only of null plots (i.e., no association) and have them compare their observed plot to the null plots, discussing what this tells them about potential association.

How to create lineups for your classes

The nullabor R package makes creating lineups reasonably painless if you understand ggplot2 graphics. I’ve created a nullabor tutorial to help you create lineups for your classes, and am almost done with shiny apps to implement lineups in a variety of settings.