ANOVA1 Routines

Summary

Performs a one-way (single-factor) analysis of variance (ANOVA).

Declaration

Function ANOVA1(Data: TVec; GroupIndex: TVec; out p: TSample; alpha: TSample = 0.05): TANOVA1Result;

Parameter	Description
Data	Data vector of single variable.
GroupIndex	Stores group indexes.
p	Returns the significance probability of null hypothesis that two means are equal. If p is less than desired significance alpha then the result suggests the null hypothesis (two means are equal) can be rejected.

Description

Perform the one-way analysis of variance where Data vector (one variable) is indexed by a second grouping GroupIndex vector variable.

See Also
ANOVA2

Example 1

The following example will perform ANOVA on single variable with three groups (0,1,2 - stored in GroupIndex vector).

  Use MtxExpr, Math387, Regress;
  var GroupIndex : Vector;
  Data: Vector;
  ANOVARes : TANOVA1Result;
  SigProb : TSample;
  begin
    Data.SetIt(false,[1,2,3,4,5,6,7,8,9,10,11,12]);
    GroupIndex.SetIt(false,[0,0,0,0,1,1,1,1,2,2,2,2]);
    ANOVARes := ANOVA1(Data,GroupIndex,SigProb);
    // ANOVARes = (SS1:128; SS2:15; SSTotal:143;
    // Deg1:2; Deg2:9; DegTotal:11; MS1:64;
    // MS2:1.6666666667; FDist:38.4; FCrit:4.2564947291)
    // SigProb = 3.9210149408e-05
  end;

  #include "MtxVecCpp.h"
  #include "Regress.hpp"
  #include "Math387.hpp"
  void __fastcall Example()
  {
    Vector Data, GroupIndex;
    TANOVA1Result ANOVAResult;
    double signprob;
    Data->SetIt(false,OPENARRAY(TSample,(1,2,3,4,5,6,7,8,9,10,11,12)));
    GroupIndex->SetIt(false,OPENARRAY(TSample,(0,0,0,0,1,1,1,1,2,2,2,2)));
    ANOVAResult = ANOVA1(Data,GroupIndex,signprob,0.05);
    // ANOVARes = (SS1:128; SS2:15; SSTotal:143;
    // Deg1:2; Deg2:9; DegTotal:11; MS1:64;
    // MS2:1.6666666667; FDist:38.4; FCrit:4.2564947291)
    // signprob = 3.9210149408e-05
  }

  using Dew.Math;
  using Dew.Stats;
  using Dew.Stats.Units;
  namespace Dew.Examples
  {
    private void Example()
    {
      Vector Data = new Vector(0);
      Vector GroupIndex = new Vector(0);
      double signprob;
      TANOVA1Result ar;
      Data.SetIt(false, new double[] {1,2,3,4,5,6,7,8,9,10,11,12});
      GroupIndex.SetIt(false, new double[] {0,0,0,0,1,1,1,1,2,2,2,2});
      ar = Regress.ANOVA1(Data,GroupIndex,out signprob,0.05);
      // ANOVARes = (SS1:128; SS2:15; SSTotal:143;
      // Deg1:2; Deg2:9; DegTotal:11; MS1:64;
      // MS2:1.6666666667; FDist:38.4; FCrit:4.2564947291)
      // signprob = 3.9210149408e-05
    }
  }

Declaration

Function ANOVA1(Data: TMtx; out p: TSample; alpha: TSample = 0.05): TANOVA1Result;

Parameter	Description
Data	Data matrix, each column is separate group.

Description

Performs a one-way (single-factor) analysis of variance.

Example 1

The following example will perform ANOVA1 on 4 variables.

  Uses MtxExpr, Regress, Math387;
  procedure Example;
    var Data: Matrix;
    ANOVARes : TANOVA1Result;
    SigProb : TSample;
  begin
    Data.SetIt(4,4,false,[3.2, 2.5, 5.5, 7.0,
                          6.2, 12.0, 3.0, 4.1,
                          1.5, 5.7, 4.9, 3.5,
                          2.5, 3.1, 3.2, 3.4]);
    ANOVARes := ANOVA1(Data,SigProb);
    // ANOVARes = (SS1:12.771875; SS2:82.1475; SSTotal:94.919375;
    // Deg1:3; Deg2:12; DegTotal:15; MS1:4.2572916667;
    // MS2:6.845625; FDist:0.62189963176; FCrit:3.4902948195
    // SigProb = 0.614256442
  end;

  #include "MtxVecCpp.h"
  #include "Regress.hpp"
  #include "Math387.hpp"
  void __fastcall Example()
  {
    Matrix Data;
    TANOVA1Result ANOVAResult;
    double signprob;
    Data->SetIt(4,4,false,OPENARRAY(TSample,(3.2, 2.5, 5.5, 7.0,
                          6.2, 12.0, 3.0, 4.1,
                          1.5, 5.7, 4.9, 3.5,
                          2.5, 3.1, 3.2, 3.4)));
    ANOVAResult = ANOVA1(Data,signprob,0.05);
    // ANOVARes = (SS1:12.771875; SS2:82.1475; SSTotal:94.919375;
    // Deg1:3; Deg2:12; DegTotal:15; MS1:4.2572916667;
    // MS2:6.845625; FDist:0.62189963176; FCrit:3.4902948195
    // SigProb = 0.614256442
  }

  using Dew.Math;
  using Dew.Stats;
  using Dew.Stats.Units;
  namespace Dew.Examples
  {
    private void Example()
    {
      Matrix Data = new Matrix(0,0);
      double signprob;
      TANOVA1Result ar;
      Data.SetIt(4,4,false, new double[] {3.2, 2.5, 5.5, 7.0,
                          6.2, 12.0, 3.0, 4.1,
                          1.5, 5.7, 4.9, 3.5,
                          2.5, 3.1, 3.2, 3.4});
      ar = Regress.ANOVA1(Data,out signprob,0.05);
      // ar = (SS1:12.771875; SS2:82.1475; SSTotal:94.919375;
      // Deg1:3; Deg2:12; DegTotal:15; MS1:4.2572916667;
      // MS2:6.845625; FDist:0.62189963176; FCrit:3.4902948195
      // signprob = 0.614256442
    }
  }