September 2008

This article goes much against conventional wisdom about pie charts (and doughnut charts) by answering these two simple questions:

• Can we use a large number of categories in pie charts? (Yes, we can.)
• Can we make a productive use of the apparently useless doughnut chart? (Yes, we can.)

Disclaimer (Sort of…)

Let me start by declaring this: I believe that the analysis of simple proportions is, by its very nature, very limited. It only scratches the surface of the data and it is useless for serious, decision-making processes.

A circular chart is poor because the underlying message is poor. If you can run a business using pie graphs to make sense of your data please let me know what market are you in, because I want to be there too (well, not really…).

Pie chart belong to the media and to some simple presentations. Leave them there. And don’t make the charts you see in the media your role model.

The part-of-whole issue

That said, one must recognize that proportions are so pervasive and hard-wired into our brain that escaping them is almost impossible.

A circular chart conveys perfectly the idea of part-of-whole relationship. You can’t use a bar chart to show this relationship because the whole just isn’t there! Yes, you can use percentage scales, yes you can say it in the title, but it isn’t the same thing, is it?

As I wrote in my previous post on loss aversion, each chart answers a question from a different perspective. Charts are not interchangeable.

Often pie charts are used just because they may look better (this is, of course, in the eyes of the beholder) but what the user really wants/needs to know would be better answered by a bar chart. This is a problem of graphic literacy and information management. It has nothing to do with the intrinsic qualities of pie charts.

The limit of 4 to 6 categories in pie charts

There is a widespread believe that you should not use more than four to six categories in a pie chart.

That’s is wrong or, at the very least, very incomplete.

In fact, you can use as many categories as you want, and still get meaningful insights from the chart. Problem is, you must know what to do with your data (graphic literacy and information management, again), and a large number of bad charts come from this simple fact: people don’t know what to do. Garbage in, garbage out.

“The Secret Strenght of Pies”

Here comes the fun part. In an article published back in 1991 by Ian Spence and Stephan Lewandowsky, titled “Displaying Proportions and Percentages” the authors write:

“the pie chart outperforms the bar chart for complicated comparisons, suggesting that the perceptual addition and comparison of components is inherently easier with the pie chart than the bar chart.” (emphasis added)

(By the way, the authors also say that this advantage will be lost if you “explode” the slices.)

It is not difficult to believe that it is somewhat easier to sum the areas of slices in a pie than it is to imagine the combined heights of bars stacked on one another.(…) Regardless, the fact remains that a comparison of two sets of summed parts is rare in the real world. But, by all means, should you ever need to display data for this purpose, a pie chart would serve you well.

Please note that Stephen Few, in his highly regarded book “Show me the Numbers” says:

“I don’t use pie charts, and I strongly recommend that you abandon them as well.”

Few acknowledges that pie charts “could serve you well” in a very limited set of circumstances (“a comparison of two sets of summed parts is rare in the real world”).

Is it really rare? It may be, but that’s because people don’t know what to do with their data (again). Let’s see.

You have 10 or even 20 categories and you want to use them all (your loss aversion tendency?). Because 20 ungroupable categories are rare in the real world, you should be able to visually group them, using a color (hue) for each group and a different saturation for each category. By doing this, you are adding layers of detail, and the reader will be able to select the level of detail that suits his/her needs. This works best when using an interactive chart because you don’t have to label everything (just use your mouse to identify on-demand the more relevant detail categories) but even a static chart can be used (in this case, label only the relevant details).

The Consumer Expenditure Chart

I used this methodology to design the consumer expenditure chart above, with living expenditure (on the right) and discretionary expenditure (on the left).  As you can see, living expenditure accounts for almost 60% of the total. That’s something you can’t easily see with a bar chart.

Then, there is a second level of detail, where you have categories like Housing (more than half of living expenditure) or Transportation. And finally, you could use your mouse to identify those detailed categories in the outer gray ring.

I’ve added some arcs to compare the profile of total consumer units to consumer units with five or more persons. Each arc always starts at the same degree of the corresponding slice. Different proportions lead to gaps or overlaps. Please note that this is not a core feature of this chart. Just wanted to play a little with comparisons (an obvious issue: since the first arcs are closer to the center, a gap between them is different than a gap between the last arcs).

The Secret Strength of Doughnut Charts

As we saw above, pie charts are better than bar charts when comparing proportions. But, as soon as you add a second pie chart you are trying to compare proportion A1 with proportion A2, not proportions A and B of the same pie. There is a shift in the analysis and the pies become useless (use bar charts instead).

Just because you can merge both pie charts in a single doughnut chart it doesn’t mean that you gain efficiency, because the essential problems remain in place.

For many, a doughnut chart is a bad mutation of a bad chart. But if, just if, two bad’s become on good? Could a doughnut, if correctly use, become a kind of pie chart on steroids?

Let me emphasize this: never use a doughnut chart to compare series. I don’t, and I strongly recommend that you should avoid it as well… Always use a doughnut chart to add detail to a series. That’s the secret strength of doughnut charts.

And please, please, could someone write an article on doughnut charts for the English Wikipedia?

I made this chart in Excel

In case you are wondering, you can make the Consumer Expenditure chart in Excel, 2003 or 2007. Instead of the default theme colors, I used some of the colors that will be available in Chart Tamer (thanks, Andreas!).

Conclusion

Pie charts do not deserve their bad reputation. They seem to be more efficient than bar charts in some very specific tasks, like  comparing combined proportions. We should take advantage of that by adding multiple levels of detail. We shouldn’t be afraid of using a large number of categories, provided that those levels of detail are clear and meaningful.

The doughnut chart is the most misunderstood of our chart toolbox. It is seen as completely useless because two series should not be compared using circular charts, but that’s not what doughnut charts should be used for. They should be used to extend the power of pie charts, managing efficiently the level of detail that we need to add to create more insightful charts.

Is this a good way to use pie and doughnut charts? Please share your thought in the comments.

[Update: If you want to know how to create this chart (with a bonus hole-remover...) Jon has a detailed explanation here.]

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