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I've been turning this around in my head and I think the answer is to ultimately tabulate the data, but it's an interesting question so I'll still post it.

I have three sets of data of equal length. Two of these sets, call them X and Y, are plotted against each other on a scatter plot. The third set, C, is overlaid on the scatter plot as a color map. All three of these sets have a standard deviation associated with each point.

It's easy enough to denote the standard deviation as error bars on the scatter plot points. But how does one typically denote the standard deviations on the color map?

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  • $\begingroup$ Don't use colors! They are so poor at conveying quantitative values that it is hopeless to try to modify them to reflect the standard deviations. There are plenty of better choices, ranging from using better symbolism (e.g., vary the size of the point symbols instead of their color) to a different chart (e.g., use a scatterplot matrix). $\endgroup$
    – whuber
    Jul 22, 2020 at 14:25
  • $\begingroup$ @whuber also good advice! Typically I discourage using color in graphs because a) nobody does it right and b) it's hard to discriminate values. Fortunately, the use of color, while tied to physical quantities, it meant to be a semi-qualitative way to guide the reader to observe a general trend, not convey any particular values. I thought about changing the size of the points, but the data is already too clustered as it is, and a lot of the meaning would be even more obscured. $\endgroup$
    – Ben S.
    Jul 23, 2020 at 12:24
  • $\begingroup$ There are alternatives, such as transparency, hexbin plots, sunflower plots, etc. But it sounds like you might be stuck with the color requirement, which narrows your options. $\endgroup$
    – whuber
    Jul 23, 2020 at 14:08
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    $\begingroup$ I looked those plots up, and I think some of the older brains in my field would explode if they saw them. The hexbin plot is intriguing, though...I may try that and see what my coauthors think. $\endgroup$
    – Ben S.
    Jul 23, 2020 at 17:38

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When dealing with colors, it's a bit tricky to denote the error bars/uncertainty.

One way it can be done is to plot two scatterplots. One with color denoting the lower limit of the error bar, and the other with color denoting the upper error bar.


Another way to do it is to plot two scatterplots. First scatterplot uses value in C to denote their points' color, and the second scatterplot uses the error/standard deviation value to denote their points' color.


Either way, it will be still difficult for humans to mentally process error or uncertainty in terms of color, so I'd advise to seek another approach.

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  • $\begingroup$ Thanks for the advice. Unfortunately, in my field, this scatterplot with color is the typical way to represent the results of the experiments I did, so I'm stuck with it. I am going to put a table in the SI with all the values and their errors, though. $\endgroup$
    – Ben S.
    Jul 22, 2020 at 13:32

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