Statistics.ZTest Function

Z Test.

Pascal

function ZTest(const Data: TVec; const Mean: double; const Sigma: double; out hRes: THypothesisResult; out Signif: double; var ConfInt: TTwoElmReal; const hType: THypothesisType = htTwoTailed; const Alpha: double = 0.05): double;

File

Statistics

Parameters

Parameters	Description
Data	The data samples to be analyzed.
Mean	The mean to value to compare the data to.
Sigma	The standard deviation to compare the data to.
hRes	Returns the result of the null hypothesis (default assumption is that the means are equal).
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.
hType	Defines the type of the null hypothesis (left, right and two - tailed).
Alpha	Defines the desired significance level. If the significance probability (Signif) is bellow the desired significance (Alpha), the null hypothesis is rejected.

Returns

Z statistics.

Description

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

See Also

tTest

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  : double;
  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 "MtxExpr.hpp"
#include "Math387.hpp"
#include "Statistics.hpp"
void __fastcall Example()
{
  sVector data;
  data.SetIt(false, OPENARRAY(double, (3,3.5,2,3.1,10,9)));
  double signif, ZStat;
  TTwoElmReal ci;
  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
}

Statistics, Functions, Example, See Also

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