## You’ll never guess this one quick trick to diagnose problems with your graphs and then make improvements

The trick is to consider graphs as comparisons.

Here’s the story. This post from several years ago shows a confusing and misleading pair of pie charts from a Kenyan election:

The quick reaction would be to say, ha ha, pie charts. But that’s not my point here. Sure, pie charts have problems and I think they’re almost never the right way to share data. But sometimes they’re not so bad.

To see the problem with the above display, we have to go back to first principles. And, with graphs, the first principle is always to consider what comparisons you would like to display, and what comparisons does the graph facilitate.

In this example, the main goal seems to be to compare the official results to the new exit poll. Thus, there are four comparisons to be made in parallel. A second goal is to compare the four categories within each dataset.

What about the pie charts? What comparisons do they easily allow?

The most salient point of any pie chart is that the percentages add up to 100%. So the first thing the graphs do is allow each of the proportions to be visually compared to the reference points of 100%, 50%, and 0%, and also 25% and 75%. We can see pretty clearly that in each dataset there are no candidates who received more than 50%, and there are two candidates who received between 25% and 50%.

But the pair of pie charts do not make it at all easy to compare each candidate from official results to the new poll. Part of that is perverse design choices, as the locations of the four “slices” have been permuted from one pie to another. But even if that had not been done—even if the four categories had been kept in pretty much the same position in each graph, and even if the coloring had been kept consistent—it would still be very difficult to compare angles of the different pies.

Basically the only way you can do it is to compare the numbers. And in that case a table would be clearer, as the relevant pairs could be written side by side. I’d prefer a dot plot.

Why, then, the pie? Part of this must be sheer convenience: whoever made these plots happened to know to make pies. But I think it’s more than that. I think the real appeal of the pie is that it graphically shows the percentages adding up to 100. And, sure, that’s something, but in this case it doesn’t really help with what I think is the key comparison of interest.

I had the same problem with Florence Nightingale’s clock plot. People think that graph is the coolest thing in the world—the wheel of time and all that—but it doesn’t facilitate the time-series comparisons that are the real goal in that example.

So, again, the point is not simply Don’t do pie charts (although I would endorse that message).

Rather, the point is: When making graphs, think about the comparisons you want readers to be able to visualize, and then evaluate possible displays based on their performance in making such comparisons clear.

1. Keith O'Rourke says:

“The best maxim in writing[graphing], perhaps, is really to love your reader[viewer] for his[their] own sake.”

Charles S. Peirce, W1: 9, 17 March 1888

2. Kyle C says:

Note to self, use the verb “permuted” more.

• Martha (Smith) says:

Or perhaps: Don’t use “permuted” when “changed” will do?

• Andrew says:

Martha:

“Permuted” is more specific than “changed.” I can permute the numbers (1, 2, 3, 4) to, say, (1, 3, 4, 2). I can change the numbers (1, 2, 3, 4) to (1, 3, 4, 2), but I can also change them to, say (1, 1, 18, 4). In the post above I said “permute” because I was speaking specifically of a permutation, not just a change.

• Martha (Smith) says:

Yes, but the context was “the locations … were permuted”, and in this context “the locations … were changed” would also be accurate — and would be better for a lay (not mathematicalyl sophisticated) audience. I think part of the reason I made this comment was that I had just read your post on communicating statistics, where you said, “Always keep in mind your goals and your audience.”

(Also, “rearranged” would be suitable, and perhaps slightly better than “changed”.)

3. Linda Seebach says:

The Economist favors half-pie (semi-circle) charts of, say, party shares pre- and post-election, with a smaller semi-circle nested inside a larger one on the same base (and the slices in the same order). It seems admirably clear and easy to interpret.