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May 27, 2014

I Like 3-D Pie Charts

So you know I’m a faithful left-brained statistician who makes every attempt to adhere to the highest professional standards of data visualization and analysis. Graphics luminaries like Edward Tufte and Stephen Few have made very valuable contributions to the field, and I bow to their wisdom.

But I have a secret confession to make: I like three-dimensional pie charts. It’s wrong, and I don’t know why; I just like them. Actually, I may be starting to figure out why. (BTW, new research reveals that a telltale sign of having at least one geek allele is a preponderance to begin sentences with the word “actually”—we’re searching for the corresponding genes with JMP Genomics.)

We know the commandments from the graphics gods: Keep it simple. Avoid chart junk. Let the data shine through. Favor linear over spatial comparisons. Eschew volumetric distortion. Wield Ockham’s Razor. Obey these commandments at all times. 3-D pie charts are the worst offenders and have long ago been banished to graph purgatory. Few has explained.

Why do I still like them? Let me be your graph optometrist for a sec and ask that annoyingly simple question: “Better A or Better B?”

So ... Better A?

bar chart

Or ... Better B?

3-D pie chart

While a usual reply to my optometrist is “I can’t freakin' tell because of those stinging drops you just put in my eyes,” in this case, the answer for me is B.

Some more background: The purpose here is to quickly and effectively convey the dominant sources of variation in a microarray experiment. Without doubt, the bar chart A has more detail and nicely uses linear instead of spatial comparison. It’s a great graph and in fact is the default one shown for such analyses in JMP Genomics.

Why B? It takes advantage of color, aggregation and 3-D aesthetics. The labels enable immediate identification with the data instead of forcing me to eyeball down to an X-axis and tilt the head to read them. In addition, blogosphere exigencies require omission of a critical feature: interactivity. It’s a spinnable graph that comes complete with slider bars that let you adjust degree of explosion and shininess. (Thanks to JMP experts Xan Gregg, who has written about 3-D pie charts in JMP, Craige Hales and David Barbour.) The ability to personally control the graph won me over. Graph B also appears to be better suited for rapid scan viewing as recommended by Bill Cleveland. Heaven forbid: multiple 3-D pie charts!

Could it be my artistic right brain has suddenly come to life like a vampire after decades of dormancy and is in need of a consultation with Van Helsing?

This all has something to do with philosophical presuppositions. Dutch philosopher Herman Dooyeweerd and colleagues have extensively discussed 14 Aspects of Reality arranged in a specific order:

1. Numerical

2. Spatial

3. Kinematic

4. Physical

5. Biotical

6. Sensitive-psychical

7. Logical

8. Cultural-historical

9. Social

10. Economical

11. Aesthetical

12. Juridicial

13. Ethical

14. Fiducial

They make a convincing case that these ordered aspects are irreducible in the sense that you cannot eliminate any of them without getting into irrecoverable binds and self-refuting contradictions. Furthermore, nearly all philosophical conflicts throughout history have arisen from different attempts to make one of these aspects the divine/ultimate one upon which all others depend. (Such reductions have often turned Ockham’s Razor into Sweeney Todd’s.) Although there is a lot more to it, everything in creation possesses each of these aspects in varying degrees. For example, the computer on which you are reading this blog exists in space, has physical properties, has economic value, etc.

With reference to the bar and pie charts above, the bar chart relies primarily on the numerical, spatial and logical aspects, whereas the interactive pie chart adds aesthetics and kinematics. These latter two aspects make a big difference and enable the pie chart to connect with the viewer on more levels. We’re naturally drawn to things that are beautiful and exhibit pleasing colors, symmetry,and interactivity. We travel the world to engage with captivating wonders and works of art, both natural and man-made. We reward business professionals and politicians who build their careers not on the substance of their message, but by the elegance and flair with which they convey it. We play Guitar Hero and Rock Band for hours on end.

The pie chart also offers a biotic connection to various round delectables. More confessions: My wife makes the world’s best grated-apple pie, and I grew up devouring my mom’s to-die-for strawberry pie. I love pizza and cheesecake and even eat quiche from time to time. So I’m environmentally conditioned to be sorely tempted by the evil 3-D pie chart, and I’ve succumbed.

So you still prefer a bar chart? That’s fine; the gods are pleased. For now, I’m cranking up Warrant’s “Cherry Pie” on my iPod and playing with some more interactive 3-D graphics.

Community Member

Douglas M Okamoto wrote:

Cylindrical coordinate system from Wikipedia, the free encyclopedia:

"A cylindrical coordinate system is a three-dimensional coordinate system, where each point is specified by the two polar coordinates of its perpendicular projection onto some fixed plane, and by its (signed) distance from that plane.

The polar coordinates may be called the radial distance or radius, and the angular position or azimuth, respectively. The third coordinate may be called the height (if the reference plane is considered horizontal). The line perpendicular to the reference plane and goes through its origin may be called the cylindrical axis or longitudinal axis."

If pie charts are stacked bar charts transformed from Cartesian-to-polar coordinates, then 3D pie charts transformed to cylindrical polar coordinates are really cakes with third dimension equal to depth of the baking pan. The 3D pie chart is a misnomer.

In the example shown, differently colored icing on the cake adds yet a fourth dimension to the graph.

Community Member

Joe Mako wrote:

I agree adding the colors is normally not a best practice, I added them in this case to make it easier to talk about, and I agree that is likely not a valid reason to add coloring. If there were other graphs based on these same dimensions, consistent coloring across all graphs for these dimensions would assist the viewer in comparing things at a glance.

I also agree that horizontal bars are commonly better, especially in a long list. In this case, there were less than 10 dimensions, so I did not have an issue telling what bar was each dimension, and I felt the coloring helped with this.

The following are the graphs I made with your suggestions. Do you think they are more effective at telling the story? Personally, I think the coloring helped the user see where the 4 bars that I pulled out came from.

Community Member

John Munoz wrote:

Good stuff Joe. Your approach a vast improvement to what Russ put up.

What do you think about flipping the chart? As a general rule, whenever I have categorical variables that are somewhat long in length, I put them on the Y axis. I think this makes the chart easier to read (no head tilting required). Also, I kept the bar colors the same as different colors typically imply that something's different. Since each bar is its own different category already, I don't think there's a need to change up the bar colors.

If you're interested, my version of the revised chart can be viewed at:

Community Member

Daniel wrote:

I'll second the request for axis sorting. I've used the pareto plot for this before, but it is not always applicable. Please consider adding this feature to a future version!

Community Member

Andy Bechtel wrote:

As a copy editor who has proofed many graphics in my day, I have become increasingly skeptical of the value of pie charts. The "slices" often become too thin for nourishment.

I think that is the case in the example you use in this post. Here's another example from my blog:

I'm not suggesting that all pie charts are bad. But they should be used with caution.

Community Member

John Munoz wrote:

Hi Russ,

Thanks for the thought provoking blog post. I must admit, I donâ t like either chart.

Two things would improve your bar chart. First, flip it so that the variance component is on the Y axis and weighted average component on the X. Second, sort the bars from highest variance component percentage to lowest. That way, in a split second, your audience will see that variance components Array and Sex make up the bulk of variance component. In addition, your readers will also see that there are 9 distinct values for variance component, which they canâ t see from the bar chart.

Two more things. I use JMP software almost every day and I love it. It is the Swiss army knife of analytics software. But in one particularly important area, it falls flat, and I think that shortfall may have led you to wander down the dark path to the pie chart. In JMP it is not possible to easily sort a bar chart by the values of the bars. The response from tech support is to manually sort the values. Since sorting is such a powerful way to show relationships in data, Iâ m surprised the good folks at JMP havenâ t made a hot fix for this shortfall. Second, Iâ ve put out a revised version of your bar chart on my blog so you can compare your version to mine. To see the difference, go to:

Community Member

Daniel wrote:

What I hear you saying (after all the blasphemy about pie charts) is that looks do matter, and we can either engage or alienate our audience with how the graph appears. And on that subject, I can agree. Our charts should be thoughfully constructed to accurately represent the data, and we should make them pleasing to the eye in so far as we do not distract or distort the underlying meaning.

Everyone who makes a chart has the choice to distort the data, and many do either unwittingly or for their own gain. We have the same choice with the aesthetic quality. Just as 3D for its own sake is wasteful or misleading, a spartan eye-sore fails at its intended mission: communicating to a viewer. To communicate effectively, your message must be true (accuracy), but you must also speak the same language the natives are speaking (style). Otherwise, they won't give your chart a second look!

The real challenge is to know your audience, and adapt accordingly.

Community Member

Lee Creighton wrote:

The problem with your argument is that you give two choices : a grayscale bar chart and a 3-D color pie chart.

These are, of course, not the only two ways of examining the quantities you present. How about adding a two-dimensional pie chart as reponse C, and ask which is the best of the three.

The human brain is not great at estimating areas, especially irregularly shaped areas. Comparing them is even harder. Adding a third dimension that distorts the irregularly shaped areas is still worse.

Community Member

Joe Mako wrote:

I do not think you are giving bar charts a fair chance with your example. A simple bar graph that is sorted and colored can produce useful insight, see . You can easily see 4 groupings: the 2 at about 50%, the 2 at about 2%, the 2 at about .2% and the 3 at 0%. You can also visually see the 5% difference between the top two.

Can you see these things looking at your 3D pie chart? I can see pie charts being useful in an interactive setting where you are drilling into the data to see what makes up that piece of the pie, but not where some of the data is represented as tiny slivers and no labels.

Also it may be useful to add filtering to "zoom" into the data points that can not be easily distinguished visually when outliers are included, see (I did not include the 3 at 0.0% because you did not include their precise values, and comparing 0 to 0 is meaningless).

Community Member

Paige wrote:

I have to disagree strenuously with this article. 3-D graphics are misleading. Much has been written why; and you gloss over the "volumetric distortion" without ever noting that this makes 3-D pie charts misleading. I note you failed to compare the bar chart to the 2D pie chart, which also does a better job than the bar chart; nor did you compare your 3-D pie chart to a 2-D pie chart. In either case, the 2-D pie chart wins for effective communications. 3-D charts are a triumph of form over substance.

Community Member

3-D Pie Reply - JMP Blog wrote:

[...] for the enlightening comments to my blog post "I Like 3-D Pie Charts" and for the new graphs. While the bar charts from Joe and John are very nice, I prefer vertical [...]

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