Statistics.tTest Function

Performs the two sample pooled or paired t-test.

Pascal

function tTest(const Data1: TVec; const Data2: TVec; out hRes: THypothesisResult; out Signif: double; var ConfInt: TTwoElmReal; Paired: boolean = false; hType: THypothesisType = htTwoTailed; Alpha: double = 0.05): double; overload;

File

Statistics

Parameters

Parameters	Description
Data1	First set of data from which to compute the mean.
Data2	Second set of data from which to compute the mean.
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.
Paired	If true, tTest routine will perform Two-Sample Paired t-Test. If false, tTest will perform Two-Sample Pooled (unpaired) t-Test.
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

The T-test statistics.

Description

It compares Data1 mean value with Data2 mean value. The assumption is Data1 and Data2 variances are equal, but unknown. The null hypothesis is that Data1 mean is equal to Data2 mean.

See Also

ZTest

Example

In this example we'll try to confirm hypothesis that first sample mean is smaller from second sample mean.

Uses Math387, MtxExpr, Statistics;
procedure Example;
var d1,d2: Vector;
  Signif  : double;
  HypRes  : THypothesisResult;
  MeanCI : TTwoElmReal;
begin
  d1.SetIt(false,[2, 3, 5, 2.5]); // mean = 3.125
  d2.SetIt([5, 7, 8]); // mean = 6.6666666667
  tTest(d1,d2, HypRes, Signif, MeanCI, false, htLeftTailed);
  // Signif = 0.01070092300; HypRes = hrReject;
  // MeanCI=[ -5.702239060933, +INF  ]
  // Comment : Since the signf is smaller than Alpha (0.05), the
  // null hypothesis (H0) that data means are equal is rejected and
  // the alternative (Ha) that d1 mean is smaller than d2 mean
  // CANNOT be rejected
end;

#include "MtxExpr.hpp"
#include "Math387.hpp"
#include "Statistics.hpp"
void __fastcall Example()
{
  sVector d1,d2;
  d1.SetIt(false, OPENARRAY(double, (2, 3, 5, 2.5))); // mean = 3.125
  d2.SetIt(false, OPENARRAY(double,(5, 7, 8))); // mean = 6.6666666667
  double signif, TStat;
  double ci[2];
  THypothesisResult hres;
  // don't use normal approximation
  TStat = TTest(d1,d2,hres,signif,ci,false,htLeftTailed,0.05);
  // signif = 0.01070092300; hres = hrReject;
  // ci=[ -5.702239060933, +INF  ]
  // Comment : Since the Signif is smaller than Alpha (0.05), the
  // null hypothesis (H0) that data means are equal is rejected and
  // the alternative (Ha) that d1 mean is smaller than d2 mean
  // CANNOT be rejected
}

Statistics, Functions, Example, See Also

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