Data Visualization

Thanks 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 bars because of their connection with the gravity orientation of trees, mountains, buildings and of course cell-phone signal strength. It’s interesting that Paige and Lee suggest 2D pie charts. Warning: The graphics gods are watching you. Daniel, I’m glad you did not sleep through Art Appreciation in college.

SAS is well known for its corporate amenities, and its cafés are no exception. I was in line for lunch the other day and came upon the always tempting dessert case. The middle shelf featured over a dozen haphazardly arranged pieces of another one of my all-time favorites: chocolate crème pie. Simply irresistible. Maybe it’s my upbringing, but I had absolutely no problem identifying the largest slice. I don’t think it’s a guy thing either, because in the extra second I took reveling about how good it was going to look on my tray, the woman behind me handily placed it on hers. How dare she! But I was smiling inwardly as I quickly grabbed the next largest one, not only because we were likely identical by state for a latent canine quantitative trait, but because I had some more assurance that at least some humans are actually decent at assessing the size of three-dimensional wedge shapes. The psychological experimental evidence cited to the contrary is largely conducted on college students who are really only good at determining how much liquid remains in bottle-shaped objects.

This has me wondering if exploding pieces of the pie chart might actually be helpful in avoiding volumetric distortion. If nothing else, exploding and appropriately labeling one or more pieces seems like a great way to emphasize them, and, conversely, leaving the really thin slices unlabeled is desirable when they are not of interest.

Regarding ordering of slices or bars, I forgot that in examples like this one there is an overriding analytical criterion. In statistical modeling in general, one typically puts main effects first, then two-way interactions, then succeeding higher order interactions and finally residual/unexplained variance. One way to accomplish this (or any other ordering) in JMP is with the Value Ordering column property. For our example, if you first run JSL code like the following…

vc_col = Column("Variance Component");

vc_col << Set Property(Value Ordering, {"Array", "Line", "Sex", "Age", 


"Line*Sex", "Line*Age", "Sex*Age", "Line*Sex*Age", "Residual"});

…then the bars appear in the desired order. We use such a column property in JMP Genomics scripts to make sure chromosome plots appear in numerical instead of alphabetical order.

If you’re having trouble comparing sizes of slices in the next pie chart you see, just pretend that it’s your favorite dessert and you’re really hungry. Works every time.

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?



Or ... Better B?



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.