How to change a part of the BoxWhiskerChart?

Question

My intention is to change the style of the bottom of the BoxWhisker Chart after drawing of the BoxWhiskerChart. For instance: lines of the BoxWhiskerChart are Thick but change to dotted bellow threshold=0.1.

The goal is to show that the part of the data is bellow the detection limit

My simple experiment

 data= RandomReal[{0, 1}, 1000];

 BoxWhiskerChart[data, {{"Whiskers", If[# < 0.1, Dashed, Thick] &}}]

anyway don't work. But my ideal is be able to change the style of the entire part of graph bellow threshold - include whiskers, quantiles, outliers... if they are < threshold.

Answer 1

You can use a custom ChartElementFunction as follows:

ClearAll[cF]
cF[t_: 0][cedf_: "BoxWhisker", o : OptionsPattern[]] := 
  ChartElementDataFunction[cedf, o][##] /. 
      l : Line[{l1 : {{x_, b_}, {x_, a_}}, l2 : {{x_, c_}, {x_, d_}}}] :> 
   {CapForm["Butt"], 
    Which[t <= a, l, t >= d, {Dashed, l}, 
      t >= c, {Line[l2 /. c -> t], Dashed, Line[l2 /. d -> t], Line[l1]},
      t <= b, {Line[l1 /. a -> t], Line[l2], Dashed, Line[l1 /. b -> t]},
      True, {Line[l2], Dashing[{Small, Small}], Line[l1]}]} &

Examples:

data = RandomReal[{0, 1}, 1000];
BoxWhiskerChart[{data, 1.2 data}, {{"Whiskers", Thick}}, 
 ChartElementFunction -> cF[.2][]]

 BoxWhiskerChart[{data, 1.2 data}, {{"Whiskers", Thick}},
   ChartElementFunction -> cF[.9]["GlassBoxWhisker"], ChartStyle->"Rainbow"]

Update: Adding dashed edges below the threshold per Okkes's suggestion in the comments:

ClearAll[cF2]
cF2[t_: 0][cedf_: "BoxWhisker", o : OptionsPattern[]] := Module[{qt = Quartiles[#2]},
  {CapForm["Butt"], ChartElementDataFunction[cedf, o][##] /. 
       l : Line[{l1 : {{x_, b_}, {x_, a_}}, l2 : {{x_, c_}, {x_, d_}}}] :> 
   Which[t <= a, l, t >= d, {Dashed, l}, 
         t >= c, {Line[l2 /. c -> t], Dashed, Line[l2 /. d -> t], Line[l1]}, 
         t <= b, {Line[l1 /. a -> t], Line[l2], Dashed, Line[l1 /. b -> t]}, 
         True, {Line[l2], Dashed, Line[l1]}], 
   Which[t >= qt[[-1]], {EdgeForm[{Dashed, Thick, Black}], FaceForm[], 
          Polygon @ {{#[[1, 1]],  qt[[-1]]}, {#[[1, 1]], qt[[1]]},
           {#[[1, 2]], qt[[1]]}, {#[[1, 2]], qt[[-1]]}}}, 
     qt[[-1]] > t > qt[[1]], {Thick, Black, 
          Line @ {{#[[1, 1]], t}, {#[[1, 1]],  qt[[-1]]}, 
           {#[[1, 2]], qt[[-1]]}, {#[[1, 2]], t}}, 
          Dashed, Line @ {{#[[1, 1]], t}, {#[[1, 1]], 
               qt[[1]]}, {#[[1, 2]], qt[[1]]}, {#[[1, 2]], t}}}, 
     True, {}]}] &

Example:

data = RandomReal[{0, 1}, 1000];
t = .85;
BoxWhiskerChart[{data, 1.5 data}, {{"Whiskers", Thick}}, 
 GridLines -> {None, {t}},
  ChartElementFunction -> cF2[t]["GradientScaleBoxWhisker", "ColorScheme" -> "Rainbow"], 
 ImageSize -> Large]