# [R] Diamond graphs

Baize, Harold HBaize at buttecounty.net
Thu Aug 21 18:45:58 CEST 2003

```Richard A. O'Keefe  <ok at cs.otago.ac.nz> wrote:

> Someone mentioned the new "Diamond Graphs" invented at Johns Hopkins.
> I haven't see the August 2003 issue of The American Statistician yet,
> but I _have_ read the press release.

Same here.

> The fact that someone would try to patent this strikes me as outrageous;
> the actual amount of novelty is so tiny.

Agree again. [Richards points edited for space]

> For R, I don't think it matters, because I think that diamond graphs
> In short, it looks to me as though "diamond graphs" are something R
> is better off without.

A few points to add to Richards comments. The proposed "diamond graph"
is not innovative, more intuitive, or more accurate than existing
graph forms.  It is applicable to one limited graphing problem: a
continuous (outcome) dimension and two discrete categorical dimensions.
Ironically, the example
http://www.jhu.edu/~gazette/2003/18aug03/18graph.html  uses artificially
imposed discrete categories on two continuous variables!
Why not treat them as continuous?

This specific problem (2 categorical, 1 continuous) presents the
challenge of representing 3 dimensions on a two dimensional plane.
The "traditional" solution is the "3D bar chart" which uses
perspective to represent the third dimension. There are many
problems with that compromise. The two greatest being that the
fixed perspective can obscure bars further back in the z (depth)
dimension, and that perception of the relative size (height) of
the bars is less precise due to projection of the third dimension
through perspective. The perspective distortion can be corrected
through stereoscopic presentation, the obstruction of bars can
be corrected through animation. These solutions complete the third
dimension, but will not work on a monochromatic printed page.

Less expensive and more practical would be to present the data in
a two dimensional matrix (as proposed in the "diamond") but not
to use an odd shape to convey the third dimension. The third
dimension could be represented by hue (color) or brightness (shade).
I suspect that actual psychometric tests would show that color
or other visual representations of density would be more accurate
and reliable than their proposed solution which confounds area with
shape.

As a caveat, I have not read the American Statistician article.
I will be surprised if they present data showing that users
can more accurately perceive variation in the continuous variable
through their odd shape solution in contrast to either color or