What do we see when we look at slices of a pie chart? Angles? Areas? Arc length? The answer to this question isn’t clear and thus “experts” recommend avoiding pie charts at all.
Robert Kosara is a Senior Research Scientist at Tableau Software (you should follow his blog https://eagereyes.org), who is very active in studying pie charts. In 2016, Robert Kosara and his collaborators published a series of studies about pie charts. There is a nice post called “An Illustrated Tour of the Pie Chart Study Results” that summarizes these studies.
Last week, Robert published another paper with a pretty confident title (“Evidence for Area as the Primary Visual Cue in Pie Charts”) and a very inconclusive conclusion
While this study suggests that the charts are read by area, itis not conclusive. In particular, the possibility of pie chart usersre-projecting the chart to read them cannot be ruled out. Furtherexperiments are therefore needed to zero in on the exact mechanismby which this common chart type is read.
Kosara. “Evidence for Area as the Primary Visual Cue in Pie Charts.” OSF, 17 Oct. 2019. Web.
The previous Kosara’s studies had strong practical implications, the most important being that pie charts are not evil provided they are done correctly. However, I’m not sure what I can take from this one. As far as I understand the data, the answer to the questions in the beginning of this post are still unclear. Maybe, the “real answer” to these questions is “a combination of thereof”.
This is another post in the series Because You Can. This time, I will claim that the fact that you can put error bars on a bar chart doesn’t mean you should.
It started with a paper by prof. Gerd Gigerenzer whose work in promoting numeracy I adore. The paper, “Natural frequencies improve Bayesian reasoning in simple and complex inference tasks” contained a simple graph that meant to convince the reader that natural frequencies lead to more accurate understanding (read the paper, it explains these terms). The error bars in the graph mean to convey uncertainty. However, the data visualization selection that Gigerenzer and his team selected is simply wrong.
First of all, look at the leftmost bar, it demonstrates so many problems with error bars in general, and in error bars in barplots in particular. Can you see how the error bar crosses the X-axis, implying that Task 1 might have resulted in negative percentage of correct inferences?
The irony is that Prof. Gigerenzer is a worldwide expert in communicating uncertainty. I read his book “Calculated risk” from cover to cover. Twice.
Why is this important?
Communicating uncertainty is super important. Take a look at this 2018 study with the self-explaining title “Uncertainty Visualization Influences how Humans Aggregate Discrepant Information.” From the paper: “Our study repeatedly presented two [GPS] sensor measurements with varying degrees of inconsistency to participants who indicated their best guess of the “true” value. We found that uncertainty information improves users’ estimates, especially if sensors differ largely in their associated variability”.
Also recall the surprise when Donald Trump won the presidential elections despite the fact that most of the polls predicted that Hillary Clinton had higher chances to win. Nobody cared about uncertainty, everyone saw the graphs!
We create visualizations to aid viewers in making visual inferences. Different visualizations are suited to different inferences. Some visualizations offer more additional perceptual inferences over comparable visualizations. That is, the specific configuration enables additional inferences to be observed directly, without additional cognitive load. (e.g. see Gem Stapleton et al, Effective Representation of Information: Generalizing Free Rides2016).
Here’s an example from 1940, a bar chart where both bar length and width indicate data:
The length of the bar (horizontally) is the percent increase in income in each industry. Manufacturing has the biggest increase in income (18%), Contract Construction is second at 13%.
The width of the bar (vertically) is the relative size of that industry: Manufacturing is wide – it’s the biggest industry – it accounts for about 23% of all industry. Contract Construction is narrow, perhaps the third smallest industry, perhaps around 3-4%.
Pseudocode is an informal high-level description of the operating principle of a computer program or other algorithm. People write pseudocode to isolate the “bigger picture” of an algorithm. Pseudocode doesn’t care about the particular implementation details that are secondary to the problem, such as memory management, dealing with different encoding, etc. Writing out the pseudocode version of a function is frequently the first step in planning the implementation of complex logic.
Similarly, I use sketches when I plan non-trivial charts, and when I discuss data visualization alternatives with colleagues or students.
One can use a sheet of paper, a whiteboard, or a drawing application. You may recognize this approach as a form of “paper prototyping,” but it deserves its own term. I suggest calling such a sketch a “pseudochart”*. Like a piece of pseudocode, the purpose of a pseudochart is to show the visualization approach to the data, not the final graph itself.
* Initially, I wanted to use the term “pseudograph” but the network scientists already took it for themselves.
** The first sentence of this post is a taken from the Wikipedia.
Both Jordan and PA use the same (Jordanian) school program. In both cases, I was surprised to discover that they almost never use Latin or Greek letters in their math notation. Not only that, the entire direction of the the mathematical notation is from right to left. Here’s an illustrative example from the Palestinian book.
The Arabic letters س (sin) and ص (saad) are used “instead of” x and y (the Arabic alphabet doesn’t have the notion of capital letters). The letter qaf (ق) is used as the archetypical function name (f). For some reason, the capital Greek Delta is here.
More interestingly, the entire math is “mirrored”, compared to the Left-To-Write world — including the operand order. Not only the operand order is “mirrored”, many other pieces of math notation are mirrored, such as the square root sign, limits and others.
Having said all that, one would expect to see the numbers on the X-axis (sorry, the س-axis) run from right to left. But no. The numbers on the graph run from left to right, similarly to the LTR world.
What about mathematics textbooks in Hebrew?
Unfortunately, I don’t have a copy of a Hebrew language book in calculus, so I will use fifth grade math book
Despite the fact that the Hebrew text flows from right to left, we (the Israelis) write our math notations from left to right. I have never saw any exceptions of this rule.
In this particular textbook, the X axis is set up from left to right. This direction is obvious in the upper example. The lower example lists months — from January to December. Despite the fact the the month names are written in Hebrew, their direction is LTR. Note that this is not an obvious choice. In many version of Excel, for example, the default direction of the X axis in Hebrew document is from right to left.
I need more examples
Do you have more examples of graphs written in Arabic, Farsi, Urdu or another RTL language? Please send them to me.
The maximum data-ink ratio principle implies that one should not use colors in their graphs if the graph is understandable without the colors. The fact that you can do something, such as adding colors, doesn’t mean you should do it. I know it. I even have a dedicated tag on this blog for that. Sometimes, however, consistent use of colors serves as a useful navigation tool in a long discussion. Keep reading to learn about the justified use of colors.
Pew Research Center is a “is a nonpartisan American fact tank based in Washington, D.C. It provides information on social issues, public opinion, and demographic trends shaping the United States and the world.” Recently, I read a report prepared by the Pew Center on the religious divide in the Israeli society. This is a fascinating report. I recommend reading without any connection to data visualization.
But this post does not deal with the Isreali society but with graphs and colors.
Look at the first chart in that report. You may see a tidy pie chart with several colored segments.
Aha! Can’t they use a single color without losing the details? Of course the can! A monochrome pie chart would contain the same information:
In most of the cases, such a transformation would make a perfect sense. In most of the cases, but not in this report. This report is a multipage research document packed with many facts and analyses. The pie chart above is the first graph in that report that provides a broad overview of the Israeli society. The remaining of this report is dedicated to the relationships between and within the groups represented by the colorful segments in that pie chart. To help the reader navigating through this long report, its authors use a consistent color scheme that anchors every subsequent graph to the relevant sections of the original pie chart.
All these graphs and tables will be readable without the use of colors. Despite the fact that the colors here are redundant, this is a useful redundancy. By using the colors, the authors provided additional information layers that make the navigation within the document easier. I learned about the concept of useful redundancy from “Trees, Maps, and Theorems” by Jean-luc Dumout. If you can only read one book about data communication, it should be this book.