Bar chart scale in multi-chart visualisation

Question

This is a rewording of a previous question which probably wasn't very well explained, and so didn't get any responses(!). I'm trying to create a chart which shows the smooth kernel distribution of three datasets, a box and whisker chart (below) and the histogram of the datasets laid under the kernel distribution. However, because the data is quite close to each other, I've arrange the 'histogram' into a bar chart so that the data can be displayed side by side (rather than stacked or overlapping, which is confusing with this data).

I've managed to get all three charts to show up (with some much appreciated help from others on this site), but the bar chart (histogram) is completely the wrong scale. (See image below)

When I break them down and display the charts separately though, the scaling is fine:

Here is the code:

S086 = {33.00, 55.74, 46.68, 22.26, 45.05, 41.95, 82.26, 58.79, 30.89,30.89,47.21, 30.16, 17.16, 28.05, 25.63}
T086 = {34.65, 28.52, 9.77, 38.58, 32.03, 22.26, 35.16, 45.26, 21.71,29.26, 34.71, 22.16}
X086 = {23.41, 48.54, 32.97, 28.57, 23.35, 20.70, 35.49, 21.97, 29.81,17.65, 16.73, 15.32, 16.00}
datasets = {{S086}, {T086}, {X086}}
bin = HistogramList[Flatten[datasets]][[1]]

and then (I've removed the box chart to simplify the code)

Show[
Plot[140 PDF[SmoothKernelDistribution[#], x] & /@ {S086, T086, 
  X086}, {x, 0, 100}, Evaluated -> True, 
PlotStyle -> {{Thickness[0.01], 
   RGBColor[0.23, 0.42, 0.63]}, {Thickness[0.01], 
   RGBColor[0.29, 0.53, 0.80]}, {Thickness[0.01], 
   RGBColor[0.62, 0.73, 0.88]}}, Frame -> True, 
GridLines -> Automatic], 
BarChart[Transpose@(BinCounts[#, {bin}] & /@ {S086, T086, X086}), 
Axes -> False, 
ChartStyle -> {Opacity[0.75, RGBColor[0.23, 0.42, 0.63]], 
  Opacity[0.75, RGBColor[0.29, 0.53, 0.80]], 
  Opacity[0.75, RGBColor[0.62, 0.73, 0.88]]}, 
PlotRange -> Automatic, PlotRangePadding -> None]]

Answer 1

Histogram does not support a grouped ChartLayout. Hence the workaround using BarChart:

I've arranged the 'histogram' into a bar chart so that the data can be displayed side by side.

An alternative to using BarChart with "Grouped" layout is to use a custom ChartElementFunction to produce the desired Histogram layout:

ClearAll[groupedHistogram]
groupedHistogram[cef_: "Rectangle", opts : OptionsPattern[]][n_: 1, 
   s_: {0, 0}][{{xmin_, xmax_}, {ymin_, ymax_}}, y_, {i_Integer}] := 
 ChartElementDataFunction[cef][ With[{x0 = xmin + s[[1]] (xmax - xmin)/n, 
    x1 = xmax -  s[[1]] (xmax - xmin)/n}, 
     {x0 + (x1 - x0)/n {s[[2]] + i - 1, i - s[[2]]}, {ymin, ymax}}], y]

Examples:

data1 = RandomVariate[NormalDistribution[0, 1], 500];
data2 = RandomVariate[NormalDistribution[1, 1/2], 500];
data3 = RandomVariate[NormalDistribution[2, 1], 500];
dataall = {data1, data2, data3};
Row[{Histogram[dataall, ImageSize -> 300], 
  Histogram[Thread[dataall -> Range[3]], 
    ChartElementFunction -> groupedHistogram[][3, {.3, .2}], ImageSize -> 300]}, Spacer[5]]

opdata = Thread[{S086, T086, X086} -> Range[3]];
styles = {ChartStyle -> {Red, Green, Blue}, ImageSize -> 300, Frame -> True};

Combine with SmoothHistogram using Epilog:

sh = SmoothHistogram[{S086, T086, X086}, 
   PlotStyle -> (Directive[Thick, #] & /@ {Red, Green, Blue})];

Histogram[opdata, ##& @@ styles, ChartElementFunction -> groupedHistogram[][3, {.1, 0}], 
 Epilog -> MapAt[GeometricTransformation[#, ScalingTransform[140, {0, 1}]] &,
    sh, {1}][[1]]]

Further Examples:

Histogram[opdata, ## & @@ styles, ChartElementFunction -> groupedHistogram[][3]]

Control spacings between and within groups:

Row[Histogram[opdata, ## & @@ styles, PlotLabel -> "bar spacings: " <> ToString@#,
    ChartElementFunction -> groupedHistogram[][3, #]] & /@ {{.2, .0}, {.1, .1}}, Spacer[5]]

Combine with built-in ChartElementDataFunctions for Histogram:

Row[Histogram[opdata, ##& @@ styles, PlotLabel -> "chart element function: " <> #, 
    ChartElementFunction -> groupedHistogram[#][Length@dd, {.1, .1}]] & /@
     {"ArrowRectangle", "FadingRectangle"}, Spacer[5]]

Use alternative bin specifications:

Row[Histogram[opdata, #, ##& @@ styles, PlotLabel -> "bins: " <> ToString@#, 
    ChartElementFunction -> groupedHistogram[][Length@dd, {.1, .1}]] & /@ 
      {Automatic, {Range[0, 100, 20]}}, Spacer[5]]

Use alternative height specs:

Row[Histogram[opdata, Automatic, #, ##& @@ styles, PlotLabel -> "height :" <> #, 
    ChartElementFunction -> groupedHistogram[][3, {.1, .1}]] & /@ 
     {"Probability", "SurvivalCount"}, Spacer[5]]

Answer 2

Rather than Show, you can use Prolog + Inset with Scaled:

Plot[
 140 PDF[SmoothKernelDistribution[#], x] & /@ {S086, T086, X086}, {x, 0, 100}, 
 Evaluated -> True,
 PlotStyle -> {
   {Thickness[0.01], RGBColor[0.23, 0.42, 0.63]},
   {Thickness[0.01], RGBColor[0.29, 0.53, 0.80]}, 
   {Thickness[0.01], RGBColor[0.62, 0.73, 0.88]}},
 Frame -> True,
 GridLines -> Automatic,
 Prolog -> Inset[
   BarChart[
    Transpose[BinCounts[#, {0, 100, 10}] & /@ {S086, T086, X086}],
    Axes -> False,
    BarSpacing -> {0, 1},
    ChartStyle -> {
      Opacity[0.75, RGBColor[0.23, 0.42, 0.63]], 
      Opacity[0.75, RGBColor[0.29, 0.53, 0.80]],
      Opacity[0.75, RGBColor[0.62, 0.73, 0.88]]}],
   Scaled@{0, 0},
   Scaled@{0, 0},
   Scaled@1]
]

This is a little crowded to my eye, so if use permits it, you could stack the distributions:

Plot[
 Accumulate[140 PDF[SmoothKernelDistribution[#], x] & /@ {S086, T086, X086}], {x, 0, 100},
 Evaluated -> True,
 PlotStyle -> {
   {Thickness[0.01], RGBColor[0.23, 0.42, 0.63]}, 
   {Thickness[0.01], RGBColor[0.29, 0.53, 0.80]}, 
   {Thickness[0.01], RGBColor[0.62, 0.73, 0.88]}},
 Frame -> True,
 GridLines -> Automatic,
 Prolog -> Inset[
   Histogram[
    {S086, T086, X086}, {0, 100, 10},
    Axes -> False, 
    ChartStyle -> {
      Opacity[0.75, RGBColor[0.23, 0.42, 0.63]], 
      Opacity[0.75, RGBColor[0.29, 0.53, 0.80]],
      Opacity[0.75, RGBColor[0.62, 0.73, 0.88]]},
    ChartLayout -> "Stacked"],
   Scaled@{0, 0},
   Scaled@{0, 0},
   Scaled@1]
]