Tuesday, November 27, 2012

Radar graphs: Avoid them (99.9% of the time)

Stephen Few doesn't like radar graphs, and he's not the only one who has written against them. In a recent discussion on Twitter, Jon Peltier said that they are "worse than pies" —ouch! Even Andy Kirk, who is usually as polite as a British gentleman can be, doesn't have nice words about this kind of display.

Most of the arguments against radar graphs can be summarized in a couple of sentences from this post by Graham Odds: "Even with a common scale between axes, comparing values across them remains cumbersome and error-prone. This is because rather than the simple straight-line comparison our visual perception is hard-wired to perform that is found in “conventional” chart types, comparison in radar charts requires conscious thought to mentally project a sort of arc of rotation to map a value from one axis onto another, something we are not particularly adept at."

I agree on that, something that you may find unsurprising if you have read my book already. However, I believe that there are some very specific situations in which radar graphs may be appropriate, hence the title of this post (disclaimer: I've used them just twice in my career.)

One of those cases is mentioned by Stephen Few himself at the end of his article. Another one can be illustrated with the infographic on the left, made by Matt Perry, head of graphics at the San Diego Union-Tribune. Matt sent me that page the other day, saying that he was loosely inspired by an example in The Functional Art. This one:

Época Magazine

In these two infographics, neighborhoods (Matt's piece) and Brazilian states (mine) are represented by radii arranged according to their geographical locations. We included maps in the compositions to provide some context.

The goal of both displays is to make a point: Votes for each party tend to concentrate in certain regions. In the latest Brazilian presidential election, the candidate of the Partido dos Trabalhadores (liberal: red line) won in the North East —Brazil's poorest area— by wide margins, but was tied with her main rival in other parts of the country. In San Diego, Republicans won in the northern neighborhoods, and Democrats were dominant in the southern ones.

I guess that we could argue that a parallel coordinates graph would make that message equally clear, an idea suggested by Lynn Cherny. You never know if a visual form will work until you give it a try, so I redesigned my radar graph this morning:

Not bad at all. It is certainly better if you want to accurately compare states with each other, but I have some concerns about it:

1. Is the original goal —to uncover general, regional voting patterns— as intuitively achieved as in the radar graph? I don't think so. To begin with, you need to read the labels at the bottom to identify each region. The radar graph works as a compass: North-eastern states are on the top-left; southern states are at the bottom. Besides, it is impossible to avoid certain odd features in the parallel coordinates graph: For instance, Mato Grosso (MT) and Tocantins (TO), two states that are side by side on the map, are in opposite extremes of the plot. Radar graphs look a bit more natural in these examples, as they somehow resemble the maps they are based on. Encoding the data in a parallel coordinates graph adds a needless layer of abstraction.

2. Most of the time, facilitating accurate comparisons and judgments must be our primary goal, but not always. If that were the case, we would never use choropleth maps, or proportional symbol maps, to mention just a couple of graphic forms which are adequate to reveal broad patterns. I'd recommend you to read Nathan Yau and the classic paper by Cleveland and McGill he discusses there.

Obviously, you should take my words with skepticism. This post is based on intuitions, and those rarely qualify as solid arguments, as one of greatest gems of epistemological wisdom suggests. I would love to hear your thoughts.


  1. Those graphs are pretty cool--it had never occurred to me to use a radar graph as a complement to a data map, but they work alongside each other nicely. I do think that the "parallel coordinates plot" could be improved: since the axes are the same for each observation, a dot plot is probably more appropriate (i.e. the points don't need to be connected by lines). And, as you mention, ordering the points by their geographic location probably doesn't make sense. But sorting them by one of the values (or by the difference between "red" and "blue") could show something interesting.

    One question: is a linear scale appropriate for the radar plots, or should smaller values be somewhat inflated? I ask because it's the *area* of the graph that seems to make a visual impression, not the value of each individual point. So smaller values get distorted (compare the northeast region in your plot: in the radar plot, the blue values seem much less than 25-50% of the red ones). Using square-root scales might be an improvement.

  2. Don’t you think connecting the dots suggests some kind of connection between them? That there is ”something” inbetween, or at least some kind of relation, as there is between regular variables but not between items?
    At least that is what I teach my students.
    And that is why I think there's a good reason for choosing the radar graph (the variable being further north, east, south, west …) even though it looks unfamiliar, rather than the line graph.
    Thanks for an interesting discussion!
    Ole Munk

  3. Thanks so much, Gray and Munkytalk.

    Gray, a dot plot would be an interesting option, but I believe that it would be make things harder to compare across different states/neighborhoods. You could compare the results of the parties within each of them, though. The lines help readers trace the outcomes of each party across the states. The point about linear scales is quite interesting, although I don't know if it would make things confusing for average readers.

    Munkytalk, there is indeed some kind of connection between the dots. That's actually the point of parallel coordinates graphs. It's true that they may be confusing in the first few seconds, as they seem to mimic a very well known graphic form, the time-series graph (line chart), but they don't display time-based data. But I think that, after the initial surprise, it's a graph that can be very helpful because it lets you compare the results of the parties not only within each region, but also between regions.

  4. Alberto, I love the visual style in these examples, but I'm not convinced by your defense :) Let me try using your own argument from your (excellent!) dataviz MOOC: the form of a graphic should be influenced by its function.

    In general, plots and other data summaries should group together the things that are similar. The radar plot groups together things that are on each radius outwards from the center, like spokes radiating out from a hub.

    So, if the designer has chosen a radar plot form, I assume the function is to show us a data pattern that has spatial clustering in a specific, radial way. The story should be: If you go in a straight line out from the center in any direction, most of the values in that direction will be similar.

    However, consider the Brazil choropleth above. If you go northwest from the center, the map doesn't actually have a blue spoke and a red spoke: instead you have blue on the inside, and red on the outside. So each spoke on the radar graph is averaging many blue and many red cases together, rather than finding areas that really are mostly-red or mostly-blue.

    The real pattern is "red in far northwest, red in near northwest" and this kind of pattern is obscured, not highlighted, by the radar graph. In fact, that part of the graph shows a "blue spike, red spike, blue spike" pattern. Maybe a local expert can see this pattern and tell me why it has deep meaning... but I suspect it's just statistical noise, an artifact of what you've chosen to average together, rather than a real story.

    Finally, I'm not sure how you chose the center for the radar plot, and I suspect it could look quite different if you placed the center somewhere else.

    For a better example of a useful radar graph with compass directions as the axes, I'd use a plot of average wind strength around your wind turbine, or a plot of pollution radiating out from some smoky factory. In these situations, the data are intrinsically likely to show the kind of grouping used by radar plot's averaging process, and the choice of center is not arbitrary like in the San Diego and Brazil examples above.

    Thanks for the thought-provoking post!

  5. Thanks for the comment, Jerzy, and thanks so much for participating in the course. I will have to read your message again, as I don't think I understand it. The center of these radar graphs is the 0% point (percentage of vote). It works as the 0% baseline of the dot plot. It's not a geographical center. So the farther a point is from the 0% point at the center, the more votes a particular party (red, blue, green) obtained in the state or region each axis corresponds to.

  6. Maybe I misunderstood the graphs. (Even when I click to enlarge them, the text is too small for me to read.)
    I thought that you picked some point on the map as the center of the map. Then draw a line north from that center point, find the neighborhoods it intersects, average their values together, and plot that as the "north" value on your radar plot. Then draw a new line on the map from the center heading northwest, find the neighborhoods it crosses, average them together, and plot that as the "northwest" value on your radar plot. etc...
    Is that not what you and Matt Perry did?

  7. No. These radar graphs are basically parallel coordinates graphs shaped as wheels, with each radii being a region

    1. Ah, I see now. In that case ignore my comments (although obviously I still find these graphs confusing!)
      Thanks again for a great course.

  8. Landed here from Kaiser Fung's recent post about a radar chart. In the spirit of research vs. opinion, the paper Graphical Tests for Power Comparison of Competing Designs (http://users.soe.ucsc.edu/~pang/visweek/2012/infovis/papers/hofmann.pdf) by Heike Hofmann et al. may be of interest. One of their test cases shows that circular charts underperform even for data that's naturally circular (wind direction).