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In a journal article, is it advisable to insert a colour bar (i.e. an explication of the colour scale) in a figure if arbitrary units are used? If the colour order is already stated in the legend, does a colour bar add additional information in this situation?

An example can be found in this abstract. Imagine that this figure was generated by colour-mapping a signal in arbitrary units, if the legend had specified that the colour scale goes from red (disordered) to green (ordered), would the colour bar have been useful?

Wrzlprmft
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GdV
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  • Can you give an example of a meaningful figure where the color range isn't meaningful? I'd have a hard time of this as a reviewer unless the scale was 100% normalized 0 to 1 or 100% – Bill Barth Jun 04 '16 at 21:54
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    I can imagine you are using different colours to distinguish categories on a nominal scale, but I am confused by "explication of the colour scale" and "legend" - aren't those the same thing? Hence, I second the request for an (abstract?) example. – O. R. Mapper Jun 04 '16 at 22:28
  • I've edited my post inserting an example in order to address your comments. – GdV Jun 05 '16 at 11:08

2 Answers2

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I would definitely include the color bar. It just makes things easier to read, since you can compare the displayed values directly with your eyes, rather than having to refer back to a written explanation. The bar also lets you see how the colors shade into each other as you move along the scale.

If it seems awkward to have the color bar in arbitrary units, you can explain exactly how you came by the arbitrary units (such as "data scaled by the maximum deviation from zero"). Then you can give the bar scale a more quantitative meaning. Or, you might go the other direction and just labels the ends "low" and "high."

Buzz
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An arbitrary unit is still a unit and while the absolute values of whatever quantity you are depicting are meaningless, their relations to each other are. For example, it may be relevant that a certain value is ten times as high as another one. A diagram without any scale does not only imply arbitrary units but also an arbitrary scale, which is not only useless in most cases, but it also makes me suspect that some sort of borderline beautification that was hidden from me.

This applies in particular to colour axes, for which there is no default scaling such as for geometrical axes, where I can at least suspect the axis to be linear if no further information is given. For example take this colour axis from a paper of mine:

enter image description here

As you can see, the white and pink region are more narrow than the green ones and moreover the scale is logarithmic for values larger than 1 and linear for smaller values¹. While this makes sense as it allows the reader to better see certain phenomena, it only becomes legitimate through the numbers on the colour scale that inform the reader what is going on. Otherwise I would consider this choice of scale misleading regarding the intensity of certain effects.

For these reasons, I would only use a colour axis without a scale when I would do the same if the axis were a geometrical one, which in turn I would only do if I am not actually presenting data, but illustrating a concept. But even then I would prefer a colour bar with indicators for high and low to describing such things in the caption, as it is easier to read.

¹ To be precise, all values are integer, so the exact nature of the scale between 0 and 1 does not matter.

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