StatTest

java.lang.Object
- keel.Algorithms.Statistical_Tests.Shared.StatTest

```
public class StatTest
extends java.lang.Object
```
In this class all the statistical tests and output modules are defined

Since:

JDK1.5

Version:

1.0

Author:

Written by Luciano Sanchez (University of Oviedo) 01/01/2004, Modified by Jose Otero (University of Oviedo) 01/10/2008, Modified by Amelia Zafra (University of Granada) 01/01/2006, Modified by Alberto Fernandez (University of Granada)01/01/2008, Modified by Salvador Garcia (University of Granada) 01/01/2007, Modified by Joaquin Derrac (University of Granada)29/04/2010

Nested Class Summary

Nested Classes
Modifier and Type Class and Description

class StatTest.InformationAboutClass
Class to store general information of the algorithms.

Nested Classes
Modifier and Type	Class and Description
`class`	`StatTest.InformationAboutClass` Class to store general information of the algorithms.

Field Summary

Fields
Modifier and Type	Field and Description
`static int`	`ContrastC` Classification Contrast Stat-test identifier.
`static int`	`ContrastR` Regression Contrast Stat-test identifier.
`static int`	`Dietterich5x2cvC` Classification Dietterich 5x2cv Stat-test identifier.
`static int`	`Dietterich5x2cvR` Regression Dietterich 5x2cv Stat-test identifier.
`static int`	`fC` Classification F Stat-test identifier.
`static int`	`fM` Regression F Stat-test identifier.
`static int`	`FriedmanAlignedC` Classification Aligned Friedman Stat-test identifier.
`static int`	`FriedmanAlignedR` Regression Aligned Friedman Stat-test identifier.
`static int`	`FriedmanC` Classification Friedman Stat-test identifier.
`static int`	`FriedmanI` Imbalanced Friedman Stat-test identifier.
`static int`	`FriedmanR` Regression Friedman Stat-test identifier.
`static int`	`generalC` Summary of classification data for multiple algorithms identifier.
`static int`	`generalI` Summary of data, multiple algorithms imbalanced
`static int`	`generalR` Summary of regression data for multiple algorithms identifier.
`static int`	`globalWilcoxonC` Classification Wilcoxon Stat-test identifier.
`static int`	`globalWilcoxonI` Imbalanced Wilcoxon Stat-test identifier.
`static int`	`globalWilcoxonR` Regression Wilcoxon Stat-test identifier.
`static int`	`MannWhitneyC` Classification Mann-Whitney Stat-test identifier.
`static int`	`MannWhitneyR` Regression Mann-Whitney Stat-test identifier.
`static int`	`MultipleC` Classification Multiple Stat-test identifier.
`static int`	`MultipleR` Regression Multiple Stat-test identifier.
`static int`	`QuadeC` Classification Quade Stat-test identifier.
`static int`	`QuadeR` Regression Quade Stat-test identifier.
`static int`	`ShapiroWilkC` Classification Shapiro Wilk Stat-test identifier.
`static int`	`ShapiroWilkR` Regression Shapiro Wilk Stat-test identifier.
`static int`	`summaryC` First classification algorithm summary of data identifier.
`static int`	`summaryI` Summary of data, 1 algorithm imbalanced
`static int`	`summaryR` First regression algorithm summary of data identifier.
`static int`	`tabularC` Summary of classification data for multiple algorithms identifier.
`static int`	`tabularI` Summary of data, multiple algorithms imbalanced
`static int`	`tabularR` Summary of regression data for multiple algorithms identifier.
`static int`	`tC` Classification t Stat-test identifier.
`static int`	`tR` Regression t Stat-test identifier.
`static int`	`trainTestC` Summary of data, train & test, one algorithm identifier (classification).
`static int`	`trainTestR` Summary of data, train & test, one algorithm identifier (regression).
`static int`	`WilcoxonC` Classification Wilcoxon signed ranks Stat-test identifier.
`static int`	`WilcoxonR` Regression Wilcoxon signed ranks Stat-test identifier.

Constructor Summary

Constructors
Constructor and Description
`StatTest(int selector, double[][][][] d, double[][][][] dtrain, double significance, java.lang.String nres, java.lang.String nameRel, java.util.Vector nameResults, java.lang.String[] labels)` This method calls the selected statistical test or output module.

Method Summary

All Methods Static Methods Concrete Methods
Modifier and Type	Method and Description
`static double`	`alnorm(double x, int upper)` Quoted from original Fortran documentation: Evaluates the tail area of the standardised normal curve from x to infinity if upper is true or from minus infinity to x if upper is false.
`static double`	`betainv(double x, double p, double q)` Quoted from original Fortran documentation: Computes incomplete beta function ratio for arguments x between zero and one, p and q positive.
`static double`	`correc(int i, int n)` Quoted from original Fortran documentation: Calculates correction for tail area of the i-th largest of n order statistics.
`static double`	`lnfbeta(double a, double b)` Computes natural logarithm of the beta function.
`static double`	`lnfgamma(double c)` Computes natural logarithm of the gamma function.
`static double[]`	`nscor2(int n, int n2)` Quoted from original Fortran documentation: Calculates approximate expected values of normal order statistics.
`static double`	`pf(double x, double df1, double df2)` Computes cumulative Snedecor F distribution
`static double`	`pnorm(double z, boolean upper)` Computes cumulative N(0,1) distribution.
`static double`	`pnorm(double x, boolean upper, double mu, double sigma2)` Computes cumulative N(mu,sigma) distribution.
`static double`	`poly(double[] c, int nord, double x)` Quoted from the original Fortran documentation: Calculates the algebraic polynomial of order nord-1 with array of coefficients c.
`static double`	`ppnd16(double p)` Quoted from original Fortran documentation: Produces the normal deviate Z corresponding to a given lower tail area of P; Z is accurate to about 1 part in 10**16.
`static double[]`	`testroyston(double[] x)` This method computes the statistic and the p-value of Shapiro Wilk test using Royston algorithm.
`static double[]`	`testsw(double[][][] err, double significance, java.io.PrintStream p)` Computes the p-value of Shapiro Wilk statistical test for a set of samples obtained from two algorithms and an arbitrary number of datasets
`static double[]`	`wcoef(int n, int n2)` Obtains an array of weights for calculating Shapiro Wilk statistic Translated from Fortran to C and from C to Java.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Field Detail
  - Dietterich5x2cvR
```
public static final int Dietterich5x2cvR
```
    Regression Dietterich 5x2cv Stat-test identifier.
    
    See Also:
    
    Constant Field Values
  - Dietterich5x2cvC
```
public static final int Dietterich5x2cvC
```
    Classification Dietterich 5x2cv Stat-test identifier.
    
    See Also:
    
    Constant Field Values
  - tR
```
public static final int tR
```
    Regression t Stat-test identifier.
    
    See Also:
    
    Constant Field Values
  - tC
```
public static final int tC
```
    Classification t Stat-test identifier.
    
    See Also:
    
    Constant Field Values
  - ShapiroWilkR
```
public static final int ShapiroWilkR
```
    Regression Shapiro Wilk Stat-test identifier.
    
    See Also:
    
    Constant Field Values
  - ShapiroWilkC
```
public static final int ShapiroWilkC
```
    Classification Shapiro Wilk Stat-test identifier.
    
    See Also:
    
    Constant Field Values
  - WilcoxonR
```
public static final int WilcoxonR
```
    Regression Wilcoxon signed ranks Stat-test identifier.
    
    See Also:
    
    Constant Field Values
  - WilcoxonC
```
public static final int WilcoxonC
```
    Classification Wilcoxon signed ranks Stat-test identifier.
    
    See Also:
    
    Constant Field Values
  - MannWhitneyR
```
public static final int MannWhitneyR
```
    Regression Mann-Whitney Stat-test identifier.
    
    See Also:
    
    Constant Field Values
  - MannWhitneyC
```
public static final int MannWhitneyC
```
    Classification Mann-Whitney Stat-test identifier.
    
    See Also:
    
    Constant Field Values
  - fM
```
public static final int fM
```
    Regression F Stat-test identifier.
    
    See Also:
    
    Constant Field Values
  - fC
```
public static final int fC
```
    Classification F Stat-test identifier.
    
    See Also:
    
    Constant Field Values
  - summaryC
```
public static final int summaryC
```
    First classification algorithm summary of data identifier.
    
    See Also:
    
    Constant Field Values
  - summaryR
```
public static final int summaryR
```
    First regression algorithm summary of data identifier.
    
    See Also:
    
    Constant Field Values
  - generalC
```
public static final int generalC
```
    Summary of classification data for multiple algorithms identifier.
    
    See Also:
    
    Constant Field Values
  - generalR
```
public static final int generalR
```
    Summary of regression data for multiple algorithms identifier.
    
    See Also:
    
    Constant Field Values
  - tabularC
```
public static final int tabularC
```
    Summary of classification data for multiple algorithms identifier.
    
    See Also:
    
    Constant Field Values
  - tabularR
```
public static final int tabularR
```
    Summary of regression data for multiple algorithms identifier.
    
    See Also:
    
    Constant Field Values
  - trainTestR
```
public static final int trainTestR
```
    Summary of data, train & test, one algorithm identifier (regression).
    
    See Also:
    
    Constant Field Values
  - trainTestC
```
public static final int trainTestC
```
    Summary of data, train & test, one algorithm identifier (classification).
    
    See Also:
    
    Constant Field Values
  - globalWilcoxonC
```
public static final int globalWilcoxonC
```
    Classification Wilcoxon Stat-test identifier.
    
    See Also:
    
    Constant Field Values
  - globalWilcoxonR
```
public static final int globalWilcoxonR
```
    Regression Wilcoxon Stat-test identifier.
    
    See Also:
    
    Constant Field Values
  - FriedmanC
```
public static final int FriedmanC
```
    Classification Friedman Stat-test identifier.
    
    See Also:
    
    Constant Field Values
  - FriedmanR
```
public static final int FriedmanR
```
    Regression Friedman Stat-test identifier.
    
    See Also:
    
    Constant Field Values
  - FriedmanAlignedC
```
public static final int FriedmanAlignedC
```
    Classification Aligned Friedman Stat-test identifier.
    
    See Also:
    
    Constant Field Values
  - FriedmanAlignedR
```
public static final int FriedmanAlignedR
```
    Regression Aligned Friedman Stat-test identifier.
    
    See Also:
    
    Constant Field Values
  - QuadeC
```
public static final int QuadeC
```
    Classification Quade Stat-test identifier.
    
    See Also:
    
    Constant Field Values
  - QuadeR
```
public static final int QuadeR
```
    Regression Quade Stat-test identifier.
    
    See Also:
    
    Constant Field Values
  - ContrastC
```
public static final int ContrastC
```
    Classification Contrast Stat-test identifier.
    
    See Also:
    
    Constant Field Values
  - ContrastR
```
public static final int ContrastR
```
    Regression Contrast Stat-test identifier.
    
    See Also:
    
    Constant Field Values
  - MultipleC
```
public static final int MultipleC
```
    Classification Multiple Stat-test identifier.
    
    See Also:
    
    Constant Field Values
  - MultipleR
```
public static final int MultipleR
```
    Regression Multiple Stat-test identifier.
    
    See Also:
    
    Constant Field Values
  - summaryI
```
public static final int summaryI
```
    Summary of data, 1 algorithm imbalanced
    
    See Also:
    
    Constant Field Values
  - generalI
```
public static final int generalI
```
    Summary of data, multiple algorithms imbalanced
    
    See Also:
    
    Constant Field Values
  - tabularI
```
public static final int tabularI
```
    Summary of data, multiple algorithms imbalanced
    
    See Also:
    
    Constant Field Values
  - globalWilcoxonI
```
public static final int globalWilcoxonI
```
    Imbalanced Wilcoxon Stat-test identifier.
    
    See Also:
    
    Constant Field Values
  - FriedmanI
```
public static final int FriedmanI
```
    Imbalanced Friedman Stat-test identifier.
    
    See Also:
    
    Constant Field Values
- Constructor Detail
  - StatTest
```
public StatTest(int selector,
                double[][][][] d,
                double[][][][] dtrain,
                double significance,
                java.lang.String nres,
                java.lang.String nameRel,
                java.util.Vector nameResults,
                java.lang.String[] labels)
```
    This method calls the selected statistical test or output module.
    
    Parameters:
    
    selector - An int that selects the statistical test or module to be applied. The relationship value / statistical test or output module is done via the public final static variables defined at the beginning of this class
    
    d - A cubic matrix with samples values indexed by algorithm, fold and dataset
    
    dtrain - Train data
    
    significance - 1-level of the statistical test
    
    nres - Output file name
    
    nameRel - Algorithms names
    
    nameResults - Results names
    
    labels - Class labels
- Method Detail
  - alnorm
```
public static double alnorm(double x,
                            int upper)
```
    Quoted from original Fortran documentation: Evaluates the tail area of the standardised normal curve from x to infinity if upper is true or from minus infinity to x if upper is false. Translated from Fortran to C and from C to Java. Original code published in Applied Statistics (1973) vol22 no.3 Algorithm AS66
    
    Parameters:
    
    x - x value
    
    upper - an int used as a boolean
    
    Returns:
    
    The value of the tail area of the standardised normal curve
  - ppnd16
```
public static double ppnd16(double p)
```
    Quoted from original Fortran documentation: Produces the normal deviate Z corresponding to a given lower tail area of P; Z is accurate to about 1 part in 10**16. Translated from Fortran to C and from C to Java. Original code published in Applied Statistics (1988) vol37 no. 3 Algorithm AS241
    
    Parameters:
    
    p - Area value
    
    Returns:
    
    The normal deviate value corresponding to lower tail area equal to p
  - nscor2
```
public static double[] nscor2(int n,
                              int n2)
```
    Quoted from original Fortran documentation: Calculates approximate expected values of normal order statistics. Translated from Fortran to C and from C to Java. Original code published in Applied Statistics 1982) Vol.31, No.2 Algorithm 177.3
    
    Parameters:
    
    n - The sample size
    
    n2 - The number of order statistics required; must be <= n/2
    
    Returns:
    
    The first n2 expected values
  - correc
```
public static double correc(int i,
                            int n)
```
    Quoted from original Fortran documentation: Calculates correction for tail area of the i-th largest of n order statistics. Translated from Fortran to C and from C to Java. Original code published in Applied Statistics (1982) Vol.31, No.2 Algorithm 177.4
    
    Parameters:
    
    i - ith largest ranking
    
    n - Sample size
    
    Returns:
    
    The correction for tail area of the i-th largest of n order statistics.
  - wcoef
```
public static double[] wcoef(int n,
                             int n2)
```
    Obtains an array of weights for calculating Shapiro Wilk statistic Translated from Fortran to C and from C to Java. Original code published in Appl. Statist. (1982) Vol. 31, No. 2 Algorithm AS 181.1
    
    Parameters:
    
    n - The sample size
    
    n2 - The number of order statistics required; must be <= n/2
    
    Returns:
    
    The array of weights for calculating Shapiro Wilk statistic
  - poly
```
public static double poly(double[] c,
                          int nord,
                          double x)
```
    Quoted from the original Fortran documentation: Calculates the algebraic polynomial of order nord-1 with array of coefficients c. Zero order coefficient is c(1) Translated from Fortran to C and from C to Java. Original code published in Appl. Statist. (1982) Vol. 31, No. 2 Algorithm AS 181.2
    
    Parameters:
    
    c - Vector of coefficients
    
    nord - order of the polinomial + 1
    
    x - x value
    
    Returns:
    
    The value of the polinomial
  - testroyston
```
public static double[] testroyston(double[] x)
```
    This method computes the statistic and the p-value of Shapiro Wilk test using Royston algorithm. Part of the code was translated from Fortran to C and from C to Java, finally encapsulated in this method calling other 181.x Algorithms. Original code published in Appl. Statist. (1982) Vol. 31, No. 2 Algorithm AS 181
    
    Parameters:
    
    x - Vector with sample values.
    
    Returns:
    
    A vector with the statistic ([0] element) and the p-value ([1] element) of the test.
  - testsw
```
public static double[] testsw(double[][][] err,
                              double significance,
                              java.io.PrintStream p)
```
    Computes the p-value of Shapiro Wilk statistical test for a set of samples obtained from two algorithms and an arbitrary number of datasets
    
    Parameters:
    
    err - A cubic matrix with the samples values indexed by algorithm, fold and dataset
    
    significance - 1-level of the test
    
    p - Output stream for tracing purposes
    
    Returns:
    
    A vector of p-values, one for each dataset
  - lnfgamma
```
public static double lnfgamma(double c)
```
    Computes natural logarithm of the gamma function. Based on the code in "Numerical Recipes in C"
    
    Parameters:
    
    c - The argument of the gamma function
    
    Returns:
    
    The value of the natural logarithm of the gamma function.
  - lnfbeta
```
public static double lnfbeta(double a,
                             double b)
```
    Computes natural logarithm of the beta function.
    
    Parameters:
    
    a - The first argument of the beta function
    
    b - The second argument of the beta function
    
    Returns:
    
    The value of the natural logarithm of the beta function.
  - betainv
```
public static double betainv(double x,
                             double p,
                             double q)
```
    Quoted from original Fortran documentation: Computes incomplete beta function ratio for arguments x between zero and one, p and q positive. log of complete beta function, beta, is assumed to be known Original code published in Applied Statistics Vol32, No.1 Algorithm AS 63
    
    Parameters:
    
    x - x value
    
    p - The first argument of the beta function
    
    q - The second argument of the beta function
    
    Returns:
    
    The value of the incomplete beta function ratio for x with p and q arguments.
  - pf
```
public static double pf(double x,
                        double df1,
                        double df2)
```
    Computes cumulative Snedecor F distribution
    
    Parameters:
    
    x - x value
    
    df1 - Numerator degrees of freedom
    
    df2 - Denominator degrees of freedom
    
    Returns:
    
    The value of the cumulative Snedecor F(df1, df2) distribution for x
  - pnorm
```
public static double pnorm(double z,
                           boolean upper)
```
    Computes cumulative N(0,1) distribution. Based om Algorithm AS66 Applied Statistics (1973) vol22 no.3
    
    Parameters:
    
    z - x value
    
    upper - A boolean value, if true the integral is evaluated from z to infinity, from minus infinity to z otherwise
    
    Returns:
    
    The value of the cumulative N(0,1) distribution for z
  - pnorm
```
public static double pnorm(double x,
                           boolean upper,
                           double mu,
                           double sigma2)
```
    Computes cumulative N(mu,sigma) distribution.
    
    Parameters:
    
    x - x value
    
    upper - A boolean value, if true the integral is evaluated from z to infinity, from minus infinity to z otherwise
    
    mu - The mean of the distribution
    
    sigma2 - The variance of the distribution
    
    Returns:
    
    The value of the cumulative N(mu,sigma) distribution for x

Class StatTest

Nested Class Summary

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

Dietterich5x2cvR

Dietterich5x2cvC

tR

tC

ShapiroWilkR

ShapiroWilkC

WilcoxonR

WilcoxonC

MannWhitneyR

MannWhitneyC

fM

fC

summaryC

summaryR

generalC

generalR

tabularC

tabularR

trainTestR

trainTestC

globalWilcoxonC

globalWilcoxonR

FriedmanC

FriedmanR

FriedmanAlignedC

FriedmanAlignedR

QuadeC

QuadeR

ContrastC

ContrastR

MultipleC

MultipleR

summaryI

generalI

tabularI

globalWilcoxonI

FriedmanI

Constructor Detail

StatTest

Method Detail

alnorm

ppnd16

nscor2

correc

wcoef

poly

testroyston

testsw

lnfgamma

lnfbeta

betainv

pf

pnorm

pnorm