data=ExampleData[{"Statistics","BostonHomes"}][[All,{3,5,6,13,14}]];
labs={"Industrial\nPercent","NOX\nConc.","Median\nHome\nValue","Number\nof\nRooms","Poverty\nFraction"};
opts=Sequence[Frame->True,Axes->None,AspectRatio->1,PlotStyle->PointSize[Medium],FrameTicks->None,ImageSize->{60,60},PlotRange->All,Background->White];

GraphicsGrid[Table[If[i==j,ListPlot[{0},PlotStyle->None,Background->Lighter[Blue,.9],opts,Epilog->Inset@Style[labs[[i]],Bold,FontSize->12,FontFamily->"Helvetica"]],ListPlot[#,opts]&[Transpose[{data[[All,j]],data[[All,i]]}]]],{i,5},{j,5}],Spacings->{4,4}]

KendallTau[data]//MatrixForm

IndependenceTest[data[[All,2]],data[[All,3]],{"TestDataTable",{"KendallTau","SpearmanRank","HoeffdingD"}}]

CorrelationTest[data[[All,1;;2]],0,"TestDataTable"]