# Problems with pie charts

There seems to be in increasing discussion about pie charts.

The main arguments against it seem to be:

• Area is perceived with less power than length.
• Pie charts have very low data-point-to-pixel ratio

However, I think they can be somehow useful when portraying proportions. I agree to use a table in most cases but when you are writing a business report and you've just included hundreds of tables why not having a pie chart?

I include a couple of links:

In order to conclude this question I decided to build an example of pie-chart vs waffle-chart.

• I find your waffle chart unclear, because of the excessive whitespace. Apr 2, 2011 at 1:57
• Why does MAR have 5 squares and 7%, but OTHER have 7 squares and 5%? Sep 17, 2015 at 15:16
– tdc
Mar 21, 2017 at 19:45
• Also, I think the categories on the waffle chart should be read left to right, then up to down (so FAN should go across the top 3.5 rows, rather than the first 3.5 columns). We read left to right and comparing the proportions vertically is more difficult than it need be. Apr 7, 2017 at 14:38

I wouldn't say there's an increasing interest or debate about the use of pie charts. They are just found everywhere on the web and in so-called "predictive analytic" solutions.

I guess you know Tufte's work (he also discussed the use of multiple pie charts), but more funny is the fact that the second chapter of Wilkinson's Grammar of Graphics starts with "How to make a pie chart?". You're probably also aware that Cleveland's dotplot, or even a barchart, will convey much more precise information. The problem seems to really stem from the way our visual system is able to deal with spatial information. It is even quoted in the R software; from the on-line help for pie,

Cleveland (1985), page 264: “Data that can be shown by pie charts always can be shown by a dot chart. This means that judgements of position along a common scale can be made instead of the less accurate angle judgements.” This statement is based on the empirical investigations of Cleveland and McGill as well as investigations by perceptual psychologists.

Cleveland, W. S. (1985) The elements of graphing data. Wadsworth: Monterey, CA, USA.

There are variations of pie charts (e.g., donut-like charts) that all raise the same problems: We are not good at evaluating angle and area. Even the ones used in "corrgram", as described in Friendly, Corrgrams: Exploratory displays for correlation matrices, American Statistician (2002) 56:316, are hard to read, IMHO.

At some point, however, I wondered whether they might still be useful, for example (1) displaying two classes is fine but increasing the number of categories generally worsen the reading (especially with strong imbalance between %), (2) relative judgments are better than absolute ones, that is displaying two pie charts side by side should favor a better appreciation of the results than a simple estimate from, say a pie chart mixing all results (e.g. a two-way cross-classification table). Incidentally, I asked a similar question to Hadley Wickham who kindly pointed me to the following articles:

1. Spence, I. (2005). No Humble Pie: The Origins and Usage of a Statistical Chart. Journal of Educational and Behavioral Statistics, 30(4), 353–368.
2. Heer, J. and Bostock, M. (2010). Crowdsourcing Graphical Perception: Using Mechanical Turk to Assess Visualization Design. CHI 2010, April 10–15, 2010, Atlanta, Georgia, USA.

In sum, I think they are just good for grossly depicting the distribution of 2 to 3 classes (I use them, from time to time, to show the distribution of males and females in a sample on top of an histogram of ages), but they must be accompanied by relative frequencies or counts for being really informative. A table would still do a better job since you can add margins, and go beyond 2-way classifications.

Finally, there are alternative displays that are built upon the idea of pie chart. I can think of square pie or waffle chart, described by Robert Kosara in Understanding Pie Charts.

• Do you know any software that implements waffle charts? Mar 30, 2011 at 23:30
• @deps_stats Nope. If you're interested in implementing it in R, you might find some ideas in calendar heatmap.
– chl
Mar 31, 2011 at 9:46
• There's github.com/hrbrmstr/waffle now. Sep 3, 2015 at 13:37

My personal problem with pie charts is while they may be useful to show differences like this:

way too many people use it to show that:

Pie charts, like pie, may be delicious but they are not nutritious.

In addition to points made already, one is that rotating a pie chart changes perception of the size of the angles, as does changing the color.

If a pie chart has only a few categories, make a table. If it has a LOT of categories, then the slices will be too thin to see (much less to label accurately).

• (+1) Your blog contains excellent examples of dotplot vs pie-chart Mar 31, 2011 at 15:32

I think you've answered your own question for the 2nd bullet point. If you want to take up valuable real estate, so be it! However the first bullet is more important. With a bar chart the observer needs to estimate relative proportion based upon only 1 axis. With a pie chart judging along at least 2 axes are involved. And one axis is curved. I think that pie charts are used most effectively when you have many categories in the pie, with a legend, and it is not all that important to judge proportion.

• But isn't it more natural to use a pie chart for depicting market share rather than a bar chart? Despite area is perceived with less power... Mar 30, 2011 at 17:31
• @deps You are right, but it seems likely that people are comparing angles, not areas, in circular and near-circular pie charts, so the situation is not quite as bad as with area perception. Pie-like charts and "spinners" have been found to be good ways to help people think correctly about probabilities and proportions, too, so there is some possible merit in the use of pie charts. (See Decision making from a cognitive perspective (Busemeyer et al), p. 307)
– whuber
Mar 30, 2011 at 17:48
• @whuber (+1) Good that you mentioned the distinction between angle and area (I didn't notice your comment while I was writing my response).
– chl
Mar 30, 2011 at 18:21
• @deps_stats - Yes typically it is used for market share. But based upon what you already know, don't you think it's easier to manipulate the display to your own tastes with a pie chart? Mar 30, 2011 at 19:07
• I think my problem was more related to "good taste" or "page design" ie How to create a visually appealing report without sacrificing clarity? I need to add lots of tables and charts to a client, and I face the decision of using charts for this and tables for that, too many tables or too many charts. What I really need is a balance between visual appeal and good data depiction. Waffle charts seem like a very interesting alternative to pie-charts! Mar 30, 2011 at 21:52

I can think of almost no case in which a pie chart is better than a bar chart or stacked bar if you want to convey information.

I do have a theory or two on how pie charts got to be so popular. My first thought is related to PC commercials. Early PCs had text screens (24 x 80 characters), often green like old mainframe CRTs. To show off the new graphics screens that had a Red-Green-Blue pixel basis, a pie chart was ideal. A text screen could do a bar chart after a fashion, but couldn't do a remotely credible pie chart. Pie charts looked a lot more serious than showing a Mario Brothers screen, regardless of how the PC would actually be used. Thus, it seemed like every PC commercial in the late 1980s and early 1990s showed a pie chart on the monitor.

A second theory is that a bar chart or stacked bar is better if you want to convey information. But what if you don't? Then a pie chart works -- and charts with 3-D effects work even better.

Your waffle chart needs the red and blue values switched. As to the question of pie vs waffle, I lean toward waffle. With waffle charts you can still get the information across at small sizes even if the blocks blend together, the color still represents the regions.