Statistics.MBoxTest Function

M-Box test for equal covariances.

Pascal

function MBoxTest(const X1: TMtx; const X2: TMtx; out Signif: double; out hRes: THypothesisResult; out df1: Integer; out df2: Integer; const Alpha: double = 0.05): double;

File

Statistics

Parameters

Parameters	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.
Signif	(Significance level) returns the probability of observing the given result
hRes	Returns the result of the null hypothesis.
df1	Nominator degrees of freedom.
df2	Denominator degrees of freedom.
Alpha	Defines the desired significance level.

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

HotellingT2One

Example

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: double;
  hres: THypothesisResult;
  df1, df2: integer;
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, df1, df2, 0.05);
  // MB : 27,16221062
  // Sign : 0,01619810
  // Sign < Alpha meaning hres = hrReject i.e. covariance matrices are significantly different.
end;

#include "MtxExpr.hpp"
#include "Statistics.hpp"
void __fastcall Example()
{
  sMatrix 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;
  int df1, df2;
  double MB = MBoxTest(X1,X2,sign,hres, df1, df2, 0.05);
  // MB : 27,16221062
  // Sign : 0,01619810
  // Sign < Alpha meaning hres = hrReject i.e. covariance matrices are significantly different.
}

Statistics, Functions, Example, See Also

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