ANOVA2 Routine

Summary

Performs balanced two-way analysis of variance (ANOVA).

Declaration

Function ANOVA2(Data: TMtx; out pRows, pCols, pInt: TSample; Replications: Integer = 1; alpha: TSample = 0.05): TANOVA2Result;

Parameter	Description
Data	Stores the data to me analyzed.
Replications	Defines the number of rows/cols replications.
Alpha	Desired significance level.
pRows,pCols,pInt	Return the significance probability for the null hypothesis that rows, cols or interacted terms means are equal. These values have some meaning if Replications is more than 1. If any p is less than desired significance alpha then the result suggests the null hypothesis (rows mean, columns mean or interaction mean is not equal) can be rejected.

Description

Performs balanced two-way analysis of variance on ranks of data contained in Data matrix. The two-way analysis of variance compares the means of two or more rows and two or more columns. The data in different columns can be interpreted as change of one factor and data in different rows can be interpreted as changes in other factor. If there is more than one observation per row/column then you can set the number of row/column replications by changing Replications value to appropriate factor. An exception will be raised if (Data.Rows mod Replications) is not zero.

See Also
ANOVA1

Example 1

This example shows the ANOVA on data with Replications set to 1 meaning there is no interaction.

  Uses MtxExpr, Regress, Math387;
  procedure Example;
  var Data: Matrix;
    ANOVARes : TANOVA2Result;
    pRows, pCols, pInteract : TSample;
  begin
    Data.SetIt(4,4,false,
              [2.5, 3.2, 4.2, 3.9,
               1.9, 3.5, 3.6, 3.7,
               3.4, 3.5, 3.3, 3.4,
               4.2, 5.0, 3.1, 2.4]);
    ANOVARes := ANOVA2(Data,pRows,pCols,pInteract,1); // no interaction !!
    // ANOVARes =(SS1:0.505; SS2:1.37; SS3:NAN; SS4:6.555; SSTotal:8.43 ;
    // Deg1: 3; Deg2:3 ; Deg3:+NAN; Deg4:9 ; DegTotal:15 ;
    // MS1:0.16833333333 ; MS2:0.45666666667 ; MS3:+NAN ; MS4:0.72833333333 ;
    //FDist1:0.12260277778 ; FDist2:0.33260555556 ; FDist3:+NAN ;
    // FCrit1:3.8625483576 ; FCrit2:3.8625483576 ; FCrit3:+NAN ;
    // pRows: 0.94442876898
    // pCols: 0.80219818603
    // pInteract: 2.0820886898e-307
  end;

  #include "MtxVecCpp.h"
  #include "Regress.hpp"
  #include "Math.hpp"
  void __fastcall Example()
  {
    Matrix Data;
    Data->SetIt(4,4,false,OPENARRAY(TSample,(2.5, 3.2, 4.2, 3.9,
               1.9, 3.5, 3.6, 3.7,
               3.4, 3.5, 3.3, 3.4,
               4.2, 5.0, 3.1, 2.4)));
    double prows,pcols,pinteract;
    TANOVA2Result ar = ANOVA2(Data,prows,pcols,pinteract,1,0.05);
    // ar =(SS1:0.505; SS2:1.37; SS3:NAN; SS4:6.555; SSTotal:8.43 ;
    // Deg1: 3; Deg2:3 ; Deg3:+NAN; Deg4:9 ; DegTotal:15 ;
    // MS1:0.16833333333 ; MS2:0.45666666667 ; MS3:+NAN ; MS4:0.72833333333 ;
    //FDist1:0.12260277778 ; FDist2:0.33260555556 ; FDist3:+NAN ;
    // FCrit1:3.8625483576 ; FCrit2:3.8625483576 ; FCrit3:+NAN ;
    // pRows: 0.94442876898
    // pCols: 0.80219818603
    // pInteract: 2.0820886898e-307
  }

  using Dew.Math;
  using Dew.Stats;
  using Dew.Stats.Units;
  namespace Dew.Examples
  {
    private void Example()
    {
      Matrix Data = new Matrix(0,0);
      Data.SetIt(4,4,false, new double[] {2.5, 3.2, 4.2, 3.9,
               1.9, 3.5, 3.6, 3.7,
               3.4, 3.5, 3.3, 3.4,
               4.2, 5.0, 3.1, 2.4});
      TANOVA2Result ar = Regress.ANOVA2(Data,out prows, out pcols, ount pinteract, 1, 0.05);
      // ar =(SS1:0.505; SS2:1.37; SS3:NAN; SS4:6.555; SSTotal:8.43 ;
      // Deg1: 3; Deg2:3 ; Deg3:+NAN; Deg4:9 ; DegTotal:15 ;
      // MS1:0.16833333333 ; MS2:0.45666666667 ; MS3:+NAN ; MS4:0.72833333333 ;
      //FDist1:0.12260277778 ; FDist2:0.33260555556 ; FDist3:+NAN ;
      // FCrit1:3.8625483576 ; FCrit2:3.8625483576 ; FCrit3:+NAN ;
      // pRows: 0.94442876898
      // pCols: 0.80219818603
      // pInteract: 2.0820886898e-307
    }
  }

Example 2

This example shows the ANOVA on data with Replications set to 2 meaning there are two rows/cols per "cell".

  Uses MtxExpr, Regress, Math387;
  procedure Example;
  var Data: Matrix;
    ANOVARes : TANOVA2Result;
    pRows, pCols, pInteract : TSample;
  begin
    Data.SetIt(4,4,false,
              [2.5, 3.2, 4.2, 3.9,
               1.9, 3.5, 3.6, 3.7,
               3.4, 3.5, 3.3, 3.4,
               4.2, 5.0, 3.1, 2.4]);
    ANOVARes := ANOVA2(Data,pRows,pCols,pInteract,2); // replications! two rows/cols per "cell"
    // ANOVARes =(SS1:0.2025; SS2:1.37; SS3:4.4675; SS4:2.39; SSTotal:8.43 ;
    // Deg1: 1; Deg2:3 ; Deg3:3; Deg4:8 ; DegTotal:15 ;
    // MS1:0.2025 ; MS2:0.45666666667 ; MS3:1.4891666667 ; MS4:0.29875 ;
    // FDist1:0.060496875 ; FDist2:0.13642916667 ; FDist3:0.44488854167 ;
    // FCrit1:5.3176550716 ; FCrit2:4.0661805514 ; FCrit3:4.0661805514 ;
    // pRows: 0.81190529881
    // pCols: 0.93549639694
    // pInteract: 0.72753486979
  end;

  #include "MtxVecCpp.h"
  #include "Regress.hpp"
  #include "Math.hpp"
  void __fastcall Example()
  {
    Matrix Data;
    Data->SetIt(4,4,false,OPENARRAY(TSample,(2.5, 3.2, 4.2, 3.9,
               1.9, 3.5, 3.6, 3.7,
               3.4, 3.5, 3.3, 3.4,
               4.2, 5.0, 3.1, 2.4)));
    double prows,pcols,pinteract;
    TANOVA2Result ar = ANOVA2(Data,prows,pcols,pinteract,2,0.05);
    // ar =(SS1:0.2025; SS2:1.37; SS3:4.4675; SS4:2.39; SSTotal:8.43 ;
    // Deg1: 1; Deg2:3 ; Deg3:3; Deg4:8 ; DegTotal:15 ;
    // MS1:0.2025 ; MS2:0.45666666667 ; MS3:1.4891666667 ; MS4:0.29875 ;
    // FDist1:0.060496875 ; FDist2:0.13642916667 ; FDist3:0.44488854167 ;
    // FCrit1:5.3176550716 ; FCrit2:4.0661805514 ; FCrit3:4.0661805514 ;
    // pRows: 0.81190529881
    // pCols: 0.93549639694
    // pInteract: 0.72753486979
  }

  using Dew.Math;
  using Dew.Stats;
  using Dew.Stats.Units;
  namespace Dew.Examples
  {
    private void Example()
    {
      Matrix Data = new Matrix(0,0);
      Data.SetIt(4,4,false, new double[] {2.5, 3.2, 4.2, 3.9,
               1.9, 3.5, 3.6, 3.7,
               3.4, 3.5, 3.3, 3.4,
               4.2, 5.0, 3.1, 2.4});
      TANOVA2Result ar = Regress.ANOVA2(Data,out prows, out pcols, ount pinteract, 2, 0.05);
      // ar =(SS1:0.2025; SS2:1.37; SS3:4.4675; SS4:2.39; SSTotal:8.43 ;
      // Deg1: 1; Deg2:3 ; Deg3:3; Deg4:8 ; DegTotal:15 ;
      // MS1:0.2025 ; MS2:0.45666666667 ; MS3:1.4891666667 ; MS4:0.29875 ;
      // FDist1:0.060496875 ; FDist2:0.13642916667 ; FDist3:0.44488854167 ;
      // FCrit1:5.3176550716 ; FCrit2:4.0661805514 ; FCrit3:4.0661805514 ;
      // pRows: 0.81190529881
      // pCols: 0.93549639694
      // pInteract: 0.72753486979
    }
  }