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This is a favorite of mine

A rendition of a favorite graph of mine

This example is in a humorous vein (credit goes to a former professor of mine, Steven Gortmaker), but I am also interested in graphs that you feel beautifully capture and communicate a statistical insight or method, along with your ideas about same.

One entry per answer. Of course, this question is along the same line as What is your favorite "data analysis" cartoon?

Kindly provide proper credit/citations with any images you provide.

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Reporting to close as "primarily opinion-based". –  d33tah Jul 24 '14 at 13:51
@d33tah Please see the discussion about this question-become-community wiki on meta: meta.stats.stackexchange.com/questions/2113/…, particularly whuber's first comment to my question. –  Alexis Jul 24 '14 at 16:52
I gather you want an actual token, not your favorite type of graph. –  gung Aug 26 '14 at 2:01
@gung Righty-O. :) –  Alexis Aug 26 '14 at 4:30

5 Answers 5

I think that Anscombe's quartet deserves a place here as an example and reminder to always plot your data because datasets with the same numeric summaries can have very different relationships:

enter image description here

Anscombe, Francis J. (1973) Graphs in statistical analysis. American Statistician, 27, 17-21.

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Excellent. One of the great points in Anscombe's article is that the values of $R^{2}$, $\alpha$, $\beta$, and the $p$-value for $\beta$ are the same on each graph. I have supplemented his quartet in my classes with an omitted variables graph with these properties, also. :) –  Alexis Jul 23 '14 at 19:52
For other data sets that have been designed for a similarly enlightening purpose, see this question. –  Silverfish Jan 10 at 11:25

I always enjoy reading this Sankey diagram (a type of flow map) on the French invasion of Russia by Charles Joseph Minard in 1812:

Charles Joseph Minard's famous graph showing the decreasing size of the Grande Armée as it marches to Moscow (brown line, from left to right) and back (black line, from right to left) with the size of the army equal to the width of the line. Temperature is plotted on the lower graph for the return journey (multiply Réaumur temperatures by 1¼ to get Celsius, e.g. −30 °R = −37.5 °C).

enter image description here

(click on image to zoom)

In 2nd position, this 3D pie makes me laugh each time I see it:

enter image description here

It is the perfect example of how misleading a 3D visualization can be: Steve Jobs clearly used a 3D pie chart to make Apple's market share look much larger than it was:

The 19.5% market share slice for Apple's iPhone somehow looks bigger than the 21.2% market share for the mish-mash of "Other" brands.

Same Steve Jobs 3D trick on another slide:

enter image description here

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I hope not to push things here too far toward the humorous side with an early response that's in that vein (+1 for @GregSnow's theoretical answer!), but since I already have an entry in the favorite cartoons thread, I'll add a graph here.

By Jorge Cham of Piled Higher and Deeper infamy, as per the © on on the bottom right margin that I hope I'm respecting! I particularly like the existential crisis bump, because I'm an existential psychologist with interests in motivation and emotion. As such, it's my (un)professional opinion that this is pretty accurate! $\mathbf{\large ☺}$

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stress form the existential crisis is still less than "normal" stress –  Octopus Jul 24 '14 at 21:06
Yeah, I thought that seemed about right. Most people seem to be pretty good at repressing or otherwise setting aside those thoughts after a short phase of sudden insight and self-reevaluation. After all, how much can you really worry about your life choices while you're on vacation? More than this I'm sure, but this seems more normative. Of course, it's all humorous speculation, and probably no more empirical than introspection and informal observation of colleagues/others, but it's got plenty of face validity otherwise. –  Nick Stauner Jul 24 '14 at 21:20

Another famous visualization of data (we can have a semantic argument about whether it should be called a graph) is John Snow's 1854 map of cholera cases in London:

enter image description here

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A map is clearly a graph. –  kjetil b halvorsen Oct 7 '14 at 17:53
And this map clearly has bar charts on it. Fantastic! I can't believe I did not think of it (since I teach this map every quarter :). –  Alexis Oct 7 '14 at 18:05

Thinking in terms of a figure that packs a lot of information, I like this one:

enter image description here

It comes from the main page of the R Project for Statistical Computing. It won the R homepage graphics competition to be so displayed. The R code to produce it can be found by clicking on the figure on the R homepage.

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Setting aside the fact that these plots cannot be read on their own, due to an almost complete lack of labels and scales (with no possibility of connecting the seven different plots--do they even display the same data?), their reliance on green-red contrasts assures they will be totally useless to any color-blind person. This image is merely a style gallery, not an information display. –  whuber Oct 7 '14 at 17:37
@whuber, I think that's overly harsh. Certainly viewers would need to know what the types of graphs are & be familiar w/ the statistical concepts behind them. I would have chosen colorblind safe colors & would have used the 1st & 2nd factors instead of the 1st & 3rd, etc. But if you are familiar w/ these things, a lot of information is being packed into a small space. The data come from the 1888 Swiss fertility dataset. The figure could use a good legend; I'll try to add one later. –  gung Oct 7 '14 at 18:06
As you know, I am familiar with these kinds of graphics, but I am unable to learn anything from these particular instances. I think I am being overly gentle: much, much more criticism could validly be leveled at these graphics, employing principles enunciated by Bertin, Cleveland, Tufte, and others. But the principal, overriding impression they give is that by trying to cram too much into little space, they fall short of their potential to communicate and enlighten. Their message seems not to be about fertility but instead is "see what we can do with a computer!" –  whuber Oct 7 '14 at 19:09

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