SignTest Routines

Summary

One or two-sample Sign test.

Declaration

Function SignTest(Data: TVec; Median: TSample; out hRes: THypothesisResult; out Signif: TSample; out ConfInt: TTwoElmReal; hType: THypothesisType = htTwoTailed; Alpha: TSample = 0.05): TSample;

Description

Performs one-sample Sign test by comparing Data median value with given Median. The null hypothesis is that Data median is equal to Median. Additional assumption is that underlying population is continuous.

Categories

Hypothesis testing

Declaration

Function SignTest(Data1, Data2: TVec; out hRes: THypothesisResult; out Signif: TSample; out ConfInt: TTwoElmReal; hType: THypothesisType = htTwoTailed; Alpha: TSample = 0.05): TSample;

Parameter	Description
hRes	Returns the result of the null hypothesis (default assumption is that the means are equal).
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.
ConfInt	Returns the 100*(1-Alpha) percent confidence interval for the mean.
Alpha	Defines the desired significance level. If the significance probability (Signif) is bellow the desired significance (Alpha), the null hypothesis is rejected.

Result

The Sign test statistics.

Description

Performs paired Sign test. The routine tests the null hypothesis that Data1 and Data2 have equal median value.

See Also
WilcoxonSign

Example 1

In this example we'll use paired sign test to verify if both sample medians are equal.

  Uses MtxExpr, Math387, Statistics;
  procedure Example;
  var d1,d2: Vector;
    SignRes : TSample;
    HypRes  : THypothesisResult;
  begin
    d1.SetIt(false,[1,4,5,6,7,12]);
	  d2.SetIt(false,[3,3.5,2,3.1,10,9]);
	  SignTest(d1, d2, SignRes, HypRes); // SignRes = 0.6875; HypRes = hrNotReject
    // Since the SignRes is greater than Alpha (0.05), the
    // null hypothesis that two medians are equal is not rejected
  end;

  #include "MtxVecCpp.h"
  #include "Math387.hpp"
  #include "Statistics.hpp"
  void __fastcall Example();
  {
    Vector d1,d2;
    d1->SetIt(false, OPENARRAY(TSample, (1,4,5,6,7,12)));
    d2->SetIt(false, OPENARRAY(TSample,(3,3.5,2,3.1,10,9)));
    double signif, SStat;
    double ci[2];
    THypothesisResult hres;
    // don't use normal approximation
    SStat = SignTest(d1,d2,hres,signif,ci,htTwoTailed,0.05);
  }

  using Dew.Math;
  using Dew.Stats;
  using Dew.Stats.Units;
  namespace Dew.Examples
  {
    private void Example()
    {
      Vector d1 = new Vector(0);
      Vector d2 = new Vector(0);
      d1.SetIt(false, new double[] {1,4,5,6,7,12});
      d2.SetIt(false, new double[] {3,3.5,2,3.1,10,9});
      double signif, SStat;
      double[2] ci;
      THypothesisResult hres;
      // don't use normal approximation
      SStat = Statistics.SignTest(d1,d2,out hres,out signif,out ci,THypothesisType.htTwoTailed,0.05);
    }
  }