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Paul Strasser wondered: <<I'd like some ideas on displaying three
variables [for baseball players] on a piece of paper in such a way that
the result is as easy to comprehend as two variables are in your basic
x-y axis graph.>>
Can't be done. <g> I'm actually saying that semi-seriously, since very
few people are good at comparing three simultaneously varying
variables. It's just not something that comes naturally, and even with
training, it's a bit of a mental stretch until you've practised it for
a while. (I say this as a former scientist who watched many
colleagues--not to mention me--grapple with the problem of interpreting
3D relationships.)
If you actually want to show the numbers rather than their behavior, a
table is by far the simplest means of presentation. Any 3D presentation
creates a distortion of the values because it's inordinately (pun not
intended) difficult to extrapolate along multiple graphical axes in
three dimensions. Try it some time with a group of friends and
calculate the standard deviation of the group's estimates. Scary.
That being said, there are two good possibilities. The first is the
"response surface"--basically a topographical map of the three
variables, displayed in perspective view. Unlike 3D bar charts, which
are evil, this graph lets you see the dips and peaks in the values for
any given combination of the three variables; the angle of the lines
around each dip and peak provides a qualitative indication of the
sharpness and direction of the change. You can't easily discern the
magnitude of the change or precisely compare numbers between peaks and
valleys, but you can at least see the direction of the change.
Spider (radar) graphs are probably the best way to show this: they're
both simpler to interpret and easier to use for objective
(quantitative) comparisons. These graphs are built by creating one axis
per variable, then distributing these axes at equal angular intervals
around a circle, with each axis starting at the center of the circle.
So for example, with three axes, you'd have something that looks like
the hood ornament on a Mercedes. Choose a different line color or
pattern for each player you'll display on these axes, then connect the
points along each axis for that player, and you get a visually simple,
elegant way of comparing the different players. Of course, this gets
nasty if you have more than a few players because the lines interweave
like copulating octopuses. <g>
<<Sure, I can just make three vertical (or horizontal) bar graphs, one
for each variable, but there is a certain lack of elegance in such a
prosaic graph.>>
Depends on what you mean by "elegance". I consider successful
communication "elegant", and a bar chart (with the bar's for each
player's set of skills grouped side by side above that player's name)
is an extremely effective way to present the information. If you want
it visually elegant, screen in a faint graphic of a ball player behind
the bars, where it creates visual interest without interfering with
visual comparison of the data.
--Geoff Hart ghart -at- videotron -dot- ca
(try geoffhart -at- mac -dot- com if you don't get a reply)
