Explore Properties of Hypothesis Tests

A Monte Carlo simulation comparing the power of four goodness-of-fit tests. Points in the white region represent correct conclusions for both tests. Points above or to the right of the white region represent type II errors for the test on the vertical and horizontal axes respectively.
 In[1]:= Xdata = RandomVariate[StudentTDistribution[3], {200, 50}];
 In[2]:= Xtests = {"Kuiper", "CramerVonMises", "KolmogorovSmirnov", "PearsonChiSquare"}; pvs = Table[(DistributionFitTest[#1, Automatic, i] &) /@ data, {i, tests}]; \[Alpha] = 0.2; conclusions[\[Alpha]_] := Show[Graphics[{White, Rectangle[{0, 0}, {\[Alpha], \[Alpha]}]}], Graphics[{Lighter[Blue, .7], Rectangle[{0, \[Alpha]}, {1, 1}]}], Graphics[{Opacity[.3], Darker[Orange, .7], Rectangle[{\[Alpha], 0}, {1, 1}]}]];
 In[3]:= XGrid[Partition[ MapThread[ Show[conclusions[\[Alpha]], ListPlot[Transpose[{pvs[[#1]], pvs[[#2]]}], AspectRatio -> 1, PlotStyle -> Black], Frame -> True, FrameLabel -> {Style[tests[[#1]], FontFamily -> "Verdana", Bold, Darker[Orange, .5]], Style[tests[[#2]], FontFamily -> "Verdana", Bold, Darker[LightBlue, .5]]}] &, {{1, 1, 1, 2, 2, 3}, {2, 3, 4, 3, 4, 4}}], 3]]
 Out[3]=