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I would like to make a following chart

BoxWhiskerChart with log y-axis

Ideally I would also like to control the boxes position on a logarithmic x-axis.

Some inspiration how to do the latter may be found in the answer to my other question: How to controll position on the x-axis of a boxWhiskerChart


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Seems like you'll have to build such a plot from scratch, I see no easy way to use the existing functionality. This means working directly with Graphics primitives to construct the display. – Jens Jan 31 '13 at 18:59
@Jens crap. How come gnuplot has it and mathematica don't. – JohnnyM Jan 31 '13 at 19:55
@Jens there is a way: the option ScalingFunctions. I've added an answer detailing how it works. – rcollyer Feb 1 '13 at 3:05
up vote 14 down vote accepted

Buried in the Details section of the documentation for BoxWhiskerChart is a reference to an option called ScalingFunctions which when set "the data coordinate is scaled using s." So, first some data:

data = RandomVariate[RayleighDistribution[RandomInteger[500]], {8, 50}];

without the scaling functions:

BoxWhiskerChart[data, "Outliers", ChartStyle -> 56]

Mathematica graphics

and with ScalingFunctions set to "Log":

BoxWhiskerChart[data, "Outliers", ChartStyle -> 56, ScalingFunctions -> "Log"]

Mathematica graphics

You might need a custom list of FrameTicks to get the desired formatting. Some ideas to get you started can be found here, here and here.

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Great find (+1)! – Jens Feb 1 '13 at 5:28
@Jens thanks. I've been staring at these functions for a bit now, and sometimes interesting things appear. – rcollyer Feb 1 '13 at 5:33
Exacly what I was looking for! Awesome answer! – JohnnyM Feb 1 '13 at 14:05
This solution (ScalingFunctions) unfortunately doesn't work with the numbers less than 1(( – user10232 Dec 11 '13 at 10:36
@MaxSakharov I see the issue in v9.0.1, but it appears to work correctly in the internal betas. So, if you need the feature, I would advise upgrading when the next version comes out. – rcollyer Dec 11 '13 at 12:56

Here is an example using the commercial Presentations package (which I develop).


Here are some data sets defined by their Log10 values.

data[1] = Array[RandomReal[{0, 1}] &, 10];
data[2] = Array[RandomReal[{0, 1.5}] &, 10];
data[3] = Array[RandomReal[{-1, 1}] &, 10];
data[4] = Array[RandomReal[{-0.5, 0.5}] &, 10];
data[5] = Array[RandomReal[{-0.5, 1}] &, 10];

Here is the BoxWhisker plot code.

xticks = CustomTicks[Identity, 
   databased[{{1, "CMEE"}, {2, "CUL"}, {3, "SR"}, {4, "DR"}, {5, 
yticks = CustomTicks[
   Log10, {-1, 2, {1, 2, 5} // N, {3, 4, 6, 7, 8, 9}}];
 {{Dotted, Line[{{0, Log10[1]}, {6, Log10[1]}}]},
         ChartStyle -> 
          Directive[FaceForm[Opacity[0.2, Blue]], EdgeForm[Black], 
        CirclePoint[{0, #}, 3, Black, White] & /@ data[#]} // 
       ScaleOp[{1, 1}, {0, 0}] // TranslateOp[{#, 0}]) & /@ Range[5]},
 AspectRatio -> 0.8,
 Frame -> True,
 FrameTicks -> {{yticks, yticks // NoTickLabels}, {xticks, 
    xticks // NoTickLabels}},
 PlotLabel -> Style["BoxWhisker Chart with Log Y Scale", 13, Bold],
 ImageSize -> 400]

And here is the plot:

Mathematica graphics

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