Regress.ANOVA2 Method

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

public TANOVA2Result ANOVA2(TMtx Data, ref double pRows, ref double pCols, ref double pInt, int Replications, double alpha);

Parameters

Parameters	Description
Data	Stores the data to me analyzed.
pRows	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.
pCols	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.
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.
Replications	Defines the number of rows/cols replications.
alpha	Desired significance level.

Remarks

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.

Related Topics

ANOVA1

C# Example 1

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

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
  }
}

C# Example 2

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

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
  }
}