ZTest Routine

Summary

Z Test.

Declaration

Function ZTest(Data: TVec; Mean, Sigma: TSample; 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

Z statistic.

Description

Compares the normally distributed Data elements mean value with known standard deviation Sigma, to a mean value Mean.

See Also
TTest

Example 1

In this example we'll use Z-Test to determine if data mean and variance are equal to specific values.

  Uses MtxExpr, Math387, Statistics;
  procedure Example;
  var d: Vector;
    Signif  : TSample;
    HypRes  : THypothesisResult;
    MeanCI : TTwoElmReal;
  begin
    d.SetIt(false,[3,3.5,2,3.1,10,9]);
    ZTest(d, 5, 1.29, HypRes, Signif, MeanCI);
    // Signif = 0.84940087229; HypRes = hrNotReject;
    // MeanCI=[4.06780398958, 6.13219601041]
    // Comment : Since the SignRes is greater than Alpha (0.05), the
    // null hypothesis (H0) that data mean is equal to 5.1 cannot be rejected
    // the alternative (Ha) that data mean are NOT equal can therefore be
    // rejected
  end;

  #include "MtxVecCpp.h"
  #include "Math387.hpp"
  #include "Statistics.hpp"
  void __fastcall Example();
  {
    Vector data;
    data->SetIt(false, OPENARRAY(TSample, (3,3.5,2,3.1,10,9)));
    double signif, ZStat;
    double ci[2];
    THypothesisResult hres;
    // don't use normal approximation
    ZStat = ZTest(data, 5.0, 1.29, hres,signif,ci,htTwoTailed,0.05);
    // signif = 0.84940087229; hres = hrNotReject;
    // ci=[4.06780398958, 6.13219601041]
    // Comment : Since the SignRes is greater than Alpha (0.05), the
    // null hypothesis (H0) that data mean is equal to 5.1 cannot be rejected
    // the alternative (Ha) that data mean are NOT equal can therefore be
    // rejected
  }

  using Dew.Math;
  using Dew.Stats;
  using Dew.Stats.Units;
  namespace Dew.Examples
  {
    private void Example()
    {
      Vector data = new Vector(0);
      d1.SetIt(false, new double[] {3,3.5,2,3.1,10,9});
      double signif, ZStat;
      double[2] ci;
      THypothesisResult hres;
      // don't use normal approximation
      ZStat = Statistics.ZTest(data, 5.0, 1.29,out hres,out signif,out ci,THypothesisType.htTwoTailed,0.05);
      // signif = 0.84940087229; hres = hrNotReject;
      // ci=[4.06780398958, 6.13219601041]
      // Comment : Since the SignRes is greater than Alpha (0.05), the
      // null hypothesis (H0) that data mean is equal to 5.1 cannot be rejected
      // the alternative (Ha) that data mean are NOT equal can therefore be
      // rejected
    }
  }