ShapiroFrancia Routine

Summary

The Shapiro-Francia test for normality of data.

Declaration

Function ShapiroFrancia(Data: TVec; out hRes: THypothesisResult; out Signif: TSample; hType: THypothesisType = htTwoTailed; Alpha: TSample = 0.05): TSample;

Parameter	Description
Data	Data vector, containing ordered and unique deviates from unknown distribution.
hRes	Returns the result of the null hypothesis (default assumption is that data comes from normal distribution).
hType	Defines the type of the null hypothesis (left, right and two - tailed).
Signif	(Significance level) returns the probability of observing the given result by chance given that the null hypothesis is true.
Alpha	Defines the desired significance level. If the significance probability (Signif) is bellow the desired significance (Alpha), the null hypothesis is rejected.

Result

the Shapiro-Francia statistics.

Description

Performs the The Shapiro-Francia test for normality of data.

See Also
Unique
ShapiroWilks

Example 1

In this example we'll use Shapiro-Francia test to determine if data is coming from normal distribution.

  Uses MtxExpr, Math387, Statistics;
  procedure Example;
  var avec,bvec: Vector;
    hres: THypothesisResult;
    Signif: TSample;
  begin
    avec.Size(1000,false);
    RandomWeibull(2.5,1,avec);
    // filter original data, retain only sorted unique values
    Unique(avec,bvec);
    ShapiroFrancia(bvec,hres,signif);
    // Significance approx. 0
    // hres = hrReject -> data is not coming from normal distribution
  end;

  #include "MtxVecCpp.h"
  #include "Math387.hpp"
  #include "Statistics.hpp"
  void __fastcall Example();
  {
    Vector a,b;
    a->Size(1000,false);
    RandomWeibull(2.5,1.0,a);
    // filter original data, retain only sorted unique values
    Unique(a,b);
    THypothesisResult hres;
    double sign;
    ShapiroFrancia(b,hres, sign,htTwoTailed,0.05);
    // Significance approx. 0
    // hres = hrReject -> data is not coming from normal distribution
  }

  using Dew.Math;
  using Dew.Stats;
  using Dew.Stats.Units;
  namespace Dew.Examples
  {
    private void Example()
    {
      Vector a = new Vector(0);
      Vector b = new Vector(0);
      a.Size(1000,false);
      StatRandom.RandomWeibull(2.5,1.0,a);
      // filter original data, retain only sorted unique values
      Statistics.Unique(a,b);
      THypothesisResult hres;
      double sign;
      ShapiroFrancia(b,out hres, out sign,THypothesisType.htTwoTailed,0.05);
      // Significance approx. 0
      // hres = hrReject -> data is not coming from normal distribution
    }
  }