Living Large with Small Multiples

In the poem Song of Myself, Walt Whitman writes "Do I contradict myself? Very well then, I contradict myself. I am large, I contain multiples." And while Excel might not be considered to be as sexy as Whitman's prose, they do have some things in common. They both can contain multiples.

Small multiples use a series of similarly scaled charts. The purpose is to allow for easy comparison across time or groups. When you use these charts, you are looking at the forest and not necessarily the trees. You don't want to focus on details as much as you search for larger patterns to investigate.

I built the example below this week. It's a series of scatter plots. Each tiny blue dot is a student, and their positions on the charts represent the point where their percent attendance and scale score on the state assessment intersect. An orange line shows the linear regression for the data set in the chart. The line tells us a couple of things. It provides a quick visual on the range, as well as the basic trend.

What kinds of things do we notice? Maybe it's how students who score in Level 1, regardless of grade level, don't have much of a discernible pattern. Level 3 students tend to clump---their rates of attendance and scores are very similar to one another. Maybe we have a conversation about those areas where the line slopes downward. How do we explain a trend where the more you come to school, the worse your do on the assessment? Or maybe even the overall picture isn't what we might predict. Even those trend lines that have an upward slope aren't very steep. Wouldn't we think that better attendance leads to better scores? And maybe we need to talk about what's happening when kids get to sixth grade and attendance starts to get a lot more worse for students at all score levels.

Because you likely can't read the itty-bitty labels, I will confess that I have broken a cardinal rule when building this: the y-axes are scaled identically for each grade level, but not among all the grade levels. Percent attendance is plotted along the x-axis and is the same for all of the charts. But the range for scores changes. The higher the grade level, the higher the possible score. I've tried to mitigate this by keeping the y for each grade at about 400 points. If I'd had to make in the entire score range identical for all grade levels, the information represented was too squeezed to make sense of things.

There are thousands of students represented on this single graphic. While focusing on an individual is critical to the daily work of the classroom, small multiples serve a different purpose. This time, it's about the herd.

What will school principals see when I show this to them in a couple of weeks? I'm not sure. I'll have to provide a little support in learning to read it, but I think they'll catch on quickly enough. The chart will be part of a larger conversation around student performance...one piece of a puzzle where they will apply context. As for me, I've enjoyed looking at this because I see something different every time.

Are you using small multiples in your work? How have they been useful?

Bonus Round
To build this, I organized the necessary data and then used a pivot table and slicers to pull attendance and scale scores by grade and score level. Dynamic ranges were used for the charts, allowing for expansion/contraction of the number of data points.

Each chart was pasted into PowerPoint. This allowed me to size and position all of the charts and labels, as well as easily share the document.

Hide and Seek

I want to circle back to an article I wrote a few years ago about my favourite data visualization.

Hierarchical Cluster Analysis by Alex J. Bowers from http://www.pareonline.net/pdf/v15n7.pdf

It shows all of the grades earned by students during their K - 12 journeys in two school districts. I love this chart because it finds a way to show all of the data in a dense, but succinct, format.

In The Visual Display of Quantitative Information, Edward Tufte states that Above all else, show the data. While the quote was applied to a different concept for visualizing data, when I look at the chart above, the quote rises to the surface of my thinking. Showing the data is no small task, and as educators, we spend a lot of time and energy not doing that. We summarize the data into neat little one letter grades or one number test scores. As teachers, we might see a set of scores...but we are the only ones to do so and we typically view them as numbers, not visual displays.Things hide in numbers and number sets.

But a recent paper shared in the Public Library of Science (PLoS) makes the case that things can be hidden in simple visuals, too.

CC-BY Weissgerber, Milic, Winham, Garovic

The authors of the article Beyond Bar and Line Graphs: Time for a New Data Presentation Paradigm assert that the ever-popular bar chart is a summary, and therefore "full data may suggest different conclusions from the summary statistics."  (It reminds me of Anscombe's quartet.) We often claim that pie charts are used to hide data. Et tu, bar charts?

I won't claim that the scatterplots and bump charts in the article are ground-breaking, but this paragraph in particular caught my interest (emphasis mine):

The infrequent use of univariate scatterplots, boxplots, and histograms is a missed opportunity. The ability to independently evaluate the work of other scientists is a pillar of the scientific method. These figures facilitate this process by immediately conveying key information needed to understand the authors’ statistical analyses and interpretation of the data. This promotes critical thinking and discussion, enhances the readers’ understanding of the data, and makes the reader an active partner in the scientific process. In contrast, bar and line graphs are “visual tables” that transform the reader from an active participant into a passive consumer of statistical information. Without the opportunity for independent appraisal, the reader must rely on the authors’ statistical analyses and interpretation of the data.

As educators, we might not view our work as a scientific process, but we must engage with our data. I feel pulled between the notion above that we may be oversimplifying our data presentations and some of the research about how an audience likes their data presented---which is typically charts that are the most familiar. This is not the Great Divide, mind you. We can bring these two things together with some education in the area of data literacy.

Or perhaps we underestimate our audience. I've introduced cluster maps, bump charts, and box-and-whisker diagrams to various groups this year. The first two required very little explanation. Box-and-whiskers did require a bit more orientation, but I never felt like the group using them struggled with the interpretation. I do think that concept of engagement between the visualization and the reader, as posed by the article is important. It's a different way to view interaction---a key piece of a good quality visual. It's not that the visual need be physically interactive...people don't have to be able to click, sort, or filter every chart---but we need to at least cause some thinking about what is presented.

After reading the PLoS article, I'm more convinced than ever that we need to when and why we share all the data. Bar and line charts may well be the fast food version of data viz, but we can begin to add to our visual diet by finding ways to show all of the ingredients.

Bonus Round
If you view the article on PLoS, you will have access to two Excel workbooks to help you make the charts presented in the article.

I'll share some of my own attempts to "show the data" in coming posts. Visit bump charts and cluster charts to learn more.

A Voice from the Wilderness and the Tufte Course

Even if I don't have much to show here over the last few months, it's been a busy time of things with data viz and Excel for me. Time to catch up, don't you think?

I want to start with July, when I had the opportunity to attend a workshop by Edward Tufte---the godfather of data visualization. Business types probably don't blink at a $380 fee for a one-day course, but for someone who works in education, I was a bit worried about the cost. I looked around online for reviews of his presentations. Surely someone had attended one and blogged about it, right? But my Google Fu was weak and I didn't find one. Robert Kosara (a/k/a Eager Eyes) attended the same day I did and has posted an excellent review. I agree with many of his observations, but I also have a few notes of my own to share.

I didn't expect to be in a room with 600 people. (You don't have to bust out your spreadsheet to immediately understand that Tufte is making some serious bank with these tours.) A room this size makes the presenter more remote in some ways---you know there is no hope of any sort of personal connection. This made it all the more interesting that Tufte started the day with a little speech about how presentation is a moral act and his philosophy as a presenter. I kinda liked this idea. For years, I included my philosophy of grading as part of a syllabus, but I admit that I never really talked with students about how I see my role as a teacher (or how they saw themselves as learners...let alone how we viewed one another). While he spoke, this video played on the screen:


A lovely visual to start the day.

The rest of the day was organized around various pieces of text from his books and other videos. Tufte is very anti-presentation software...and while he called out PowerPoint in particular, there was nothing in his comments that wouldn't have applied to Keynote or Prezi. His rejection was not so much about its misuse/abuse, but rather that paper is superior because it has a higher resolution than a screen and you can include more information in a smaller space. I agree---but I also think there is room for both. They have different purposes for communication.

One of the points Tufte made throughout the day is that the onus of understanding is on the viewer. I think this is an intriguing philosophy...one that seems at odds with one of the primary purposes of data visualization. I understand the reason behind making visualizations interactive and engaging for the audience, but unless you are certain about the level of data literacy they have, leaving interpretation completely open is asking for problems.

I was disappointed in a few parts of the "workshop." One was a 30-minute commercial for his other pursuits just before lunch and another was a 45-minute discussion of big data after lunch. I felt like the former was uncalled for (dude, you already have our money) and the second seemed out of place and a bit misguided (again, assuming that the audience for data is literate about research methodology and data in general).

Am I glad I went to the workshop? Yes---not so much for the information given, but because hearing from the original person about their own ideas provides a context you can't get anywhere else. Doesn't mean I liked or agreed with everything I heard, just that my understanding has been fleshed out. Would I go again? Probably not. Presentation quality was not good and nothing new was brought to the table. Perhaps he doesn't think he owes his audience the effort---people will buy his stuff and elevate his work regardless of what he does in a workshop. But I find that disappointing.

This experience didn't stop me from going to see another guru a couple of weeks ago: Stephen Few. More on that to come.