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Visual Display of Quantitative Information
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Presenting Data and Information
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On p. 92 of Envisaging Information, ET points out that "the mind's eye does not readily give an order to ROYGBIV", and points out that shades of intensity are much easier to interpret -- more or less obvious once pointed out, but not at all obvious to people who haven't thought about it.
Now that it has become so easy to generate coloured pictures with computers, this sensible advice is more and more widely ignored. At the moment I am assessing a doctoral thesis in which the author has a graph with 1600 spots colour-coded for degrees of heterosis from 0 to more than 200%. (Heterosis is a genetic measure of the extent to which a child deviates from the average for the two parents). It's not a bad graph from the point of view of information density, but unfortunately the two darkest colours (out of five) refer to "0" and "more than 200%", with three fainter colours used for the intermediate degrees (one of them so faint as to be almost invisible). As a result it is very difficult for the eye to pick out much in the way of a pattern. With shades of grey it could have been so much better, and the author could have distinguished between more than five levels in a way that would have been intuitively clear.
-- Athel Cornish-Bowden (email)
Cynthia Brewer has great site at http://www.colorbrewer.org which allows you to specify shades to a very high degree.
-- Kate Phinney (email)
No one will ever tell me that two people see the same "red" again....
-- Ziska Childs (email)
I've never really quite agreed with that comment from ET about color, and have done a lot of experimenting. Physicists feel that the ROYBGV scale is quite natural to them, at least, though they often map color to wavelength, rather than frequency (energy), so red is "high", and blue is "low", like for the heater in your car. And there is no substitute for "rainbow" color when it comes to reading quantitative numbers off the color bar scale. But there are problems, for example with grey scale reproductions of color figures, where multi-valued scales typically destroy the data.
One solution is to use a scale called "thermal" or "black body", beginning at black, then running upward in red brightness, then adding in green and blue until it saturates at white, as anything does when heated from cold to hot. This scale increases monotonically in brightness, so it reproduces well into gray scale.
To expand on this one can have three independent brightness scales, for red, green and blue, and thereby mix another dimension or set of categories into the plot. This is often done to turn spectrally filtered images (for any wavelength range, possibly far outside the visible spectrum or for radiation other than light) into an intelligible image.
Another quantitative use of color is to associate the degree of color saturation with measurement uncertainty. Values with small uncertainties are plotted in full saturated color (on one's choice of hue scale, perhaps rainbow). Highly uncertain values are reduced in saturation to the point of gray. The result is a muddy and difficult to read image where values are highly uncertain, with saturated and easily read values corresponding to robust data. As a physicist concerned with the honesty of data displays, I especially like this approach and use it increasingly often.
It doesn't really matter whether we see the same "red" as another person, as long as we have some response to all the colors. The differences are "calibrated out" as they are in cameras and spectrometers, by observing a standard source and then agreeing upon a set of values for that source.
To close, I'd like to make a personal observation that the more different ways we plot the same data, the more likely we are to see patterns emerging that might not otherwise have been visible. I'm not convinced there is any one "correct" or "best" way to display data for this purpose. Only after the pattern emerges, does the method of display gain value. And without knowing the pattern in advance, I'm not convinced there is any way to choose the correct display method.
-- Tom Moore (email)
Today's Astronomy Picture of the Day has a nice illustration showing one shade of gray appearing to be both light and dark in an image based on its context.
-- Eric Miller (email)
I find ROYGBIV very useful in color-coding plots. In my field, it's very common to have a series of 2-D scatter plots with a varying parameter all on the same grid so I color the curves using that order (for N<7 I try to space the colors evenly) with the parameter increasing or decreasing monotonically. To my eye, that mnemonic is much easier than continually looking back at the legend to map color to parameter.
-- Matt B (email)
With regard to Tom Moore's comment about not knowing in advance what scheme will emphasize the data of greatest interest, it can be useful to interactively vary or rotate an assignment of colors, even as one may rotate a 3-d point cloud in order to find hidden structure. This can be done in Photoshop, say, or with a simple program like Eyepilot (www.colorhelper.com) -- which is a screen-overlay with tools to help the color-blind -- one of the tools just rotates the hue "wheel", and you can see features of interest "surfacing" and "submerging" as you rotate. His saturation scale is a very interesting idea (though it wouldn't work for the color-blind...) The problem in general is that hue, saturation and brightness are not independent or orthogonal in their "affect" -- and additionally, our perceptions are influenced by the words we use: pure yellow is light and pure blue is dark -- light blue is still "blue" but dark yellow is "brown" and light red is "pink".
-- Dennis Purcell (email)