MBoxTest Routine

Summary

M-Box test for equal covariances.

Declaration

Function MBoxTest(X1, X2: TMtx; out Signif: TSample; out hRes: THypothesisResult; out df1, df2: Integer; Alpha: TSample = 0.05): TSample;

Parameter	Description
X1	First matrix. The number of columns for X1 and X2 must be equal, otherwise an exception is raised.
X2	Second matrix. The number of columns for X1 and X2 must be equal, otherwise an exception is raised.
df1	Nominator degrees of freedom.
df2	Denominator degrees of freedom.

Description

Performs M-Box test for equal covariances. In this case the null hypothesis is that X1 and X2 covariances are equal and the alternative hypothesis is that X1 and X2 covariances are not equal.

See Also
HotellingT2

Example 1

Suppose we have two matrices, representing two tests with 5 samples x 3 variables. We want to test if two test matrices have the same covariances. Performing M-Box test with default significance level 5% will give us an answer.

  Uses MtxExpr, Statistics, Math387;
  procedure Example;
  var X1,X2: Matrix;
    MB,sign: TSample;
    hres: THypothesisResult;
  begin
    X1.SetIt(5,3,false,[23,45,15, 40,85,18, 215,307,60, 110,110,50, 65,105,24]);
    X2.SetIt(5,3,false,[277,230,63, 153,80,29, 306,440,105, 252,350,175, 143,205,42]);
    MB := MBoxTest(X1,X2,sign,hres);
    // MB : 27,16221062
    // Sign : 0,01619810
    // Sign < Alpha meaning hres = hrReject i.e. covariance matrices are significantly different.
  end;

  #include "MtxVecCpp.h"
  #include "Statistics.hpp"
  void __fastcall Example()
  {
    Matrix X1,X2;
    X1->SetIt(5,3,false, OPENARRAY(double, (23,45,15, 40,85,18, 215,307,60, 110,110,50, 65,105,24)));
    X2->SetIt(5,3,false, OPENARRAY(double, (277,230,63, 153,80,29, 306,440,105, 252,350,175, 143,205,42)));
    THypothesisResult hres;
    double sign;
    double MB = MBoxTest(X1,X2,sign,hres);
    // MB : 27,16221062
    // Sign : 0,01619810
    // Sign < Alpha meaning hres = hrReject i.e. covariance matrices are significantly different.
  }

  using Dew.Math;
  using Dew.Stats.Units;
  using Dew.Stats;
  namespace Dew.Examples
  {
    private void Example()
    {
      Matrix X1 = new Matrix(0,0);
      Matrix X2 = new Matrix(0,0);
      X1.SetIt(5,3,false, new double[] {23,45,15, 40,85,18, 215,307,60, 110,110,50, 65,105,24});
      X2.SetIt(5,3,false, new double[] {277,230,63, 153,80,29, 306,440,105, 252,350,175, 143,205,42});
      THypothesisResult hres;
      double sign;
      double MB = MBoxTest(X1,X2,sign,hres);
      // MB : 27,16221062
      // Sign : 0,01619810
      // Sign < Alpha meaning hres = hrReject i.e. covariance matrices are significantly different.
    }
  }