org.apache.commons.math3.stat.inference

## Class OneWayAnova

• public class OneWayAnova
extends Object
Implements one-way ANOVA (analysis of variance) statistics.

Tests for differences between two or more categories of univariate data (for example, the body mass index of accountants, lawyers, doctors and computer programmers). When two categories are given, this is equivalent to the TTest.

Uses the commons-math F Distribution implementation to estimate exact p-values.

This implementation is based on a description at http://faculty.vassar.edu/lowry/ch13pt1.html

 Abbreviations: bg = between groups,
wg = within groups,
ss = sum squared deviations

Since:
1.2
• ### Constructor Summary

Constructors
Constructor and Description
OneWayAnova()
Default constructor.
• ### Method Summary

Methods
Modifier and Type Method and Description
double anovaFValue(Collection<double[]> categoryData)
Computes the ANOVA F-value for a collection of double[] arrays.
double anovaPValue(Collection<double[]> categoryData)
Computes the ANOVA P-value for a collection of double[] arrays.
double anovaPValue(Collection<SummaryStatistics> categoryData, boolean allowOneElementData)
Computes the ANOVA P-value for a collection of SummaryStatistics.
boolean anovaTest(Collection<double[]> categoryData, double alpha)
Performs an ANOVA test, evaluating the null hypothesis that there is no difference among the means of the data categories.
• ### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• ### Constructor Detail

• #### OneWayAnova

public OneWayAnova()
Default constructor.
• ### Method Detail

• #### anovaFValue

public double anovaFValue(Collection<double[]> categoryData)
throws NullArgumentException,
DimensionMismatchException
Computes the ANOVA F-value for a collection of double[] arrays.

Preconditions:

• The categoryData Collection must contain double[] arrays.
• There must be at least two double[] arrays in the categoryData collection and each of these arrays must contain at least two values.

This implementation computes the F statistic using the definitional formula

   F = msbg/mswg
where
  msbg = between group mean square
mswg = within group mean square
are as defined here

Parameters:
categoryData - Collection of double[] arrays each containing data for one category
Returns:
Fvalue
Throws:
NullArgumentException - if categoryData is null
DimensionMismatchException - if the length of the categoryData array is less than 2 or a contained double[] array does not have at least two values
• #### anovaPValue

public double anovaPValue(Collection<double[]> categoryData)
throws NullArgumentException,
DimensionMismatchException,
ConvergenceException,
MaxCountExceededException
Computes the ANOVA P-value for a collection of double[] arrays.

Preconditions:

• The categoryData Collection must contain double[] arrays.
• There must be at least two double[] arrays in the categoryData collection and each of these arrays must contain at least two values.

This implementation uses the commons-math F Distribution implementation to estimate the exact p-value, using the formula

   p = 1 - cumulativeProbability(F)
where F is the F value and cumulativeProbability is the commons-math implementation of the F distribution.

Parameters:
categoryData - Collection of double[] arrays each containing data for one category
Returns:
Pvalue
Throws:
NullArgumentException - if categoryData is null
DimensionMismatchException - if the length of the categoryData array is less than 2 or a contained double[] array does not have at least two values
ConvergenceException - if the p-value can not be computed due to a convergence error
MaxCountExceededException - if the maximum number of iterations is exceeded
• #### anovaPValue

public double anovaPValue(Collection<SummaryStatistics> categoryData,
boolean allowOneElementData)
throws NullArgumentException,
DimensionMismatchException,
ConvergenceException,
MaxCountExceededException
Computes the ANOVA P-value for a collection of SummaryStatistics.

Preconditions:

This implementation uses the commons-math F Distribution implementation to estimate the exact p-value, using the formula

   p = 1 - cumulativeProbability(F)
where F is the F value and cumulativeProbability is the commons-math implementation of the F distribution.

Parameters:
categoryData - Collection of SummaryStatistics each containing data for one category
allowOneElementData - if true, allow computation for one catagory only or for one data element per category
Returns:
Pvalue
Throws:
NullArgumentException - if categoryData is null
DimensionMismatchException - if the length of the categoryData array is less than 2 or a contained SummaryStatistics does not have at least two values
ConvergenceException - if the p-value can not be computed due to a convergence error
MaxCountExceededException - if the maximum number of iterations is exceeded
Since:
3.2
• #### anovaTest

public boolean anovaTest(Collection<double[]> categoryData,
double alpha)
throws NullArgumentException,
DimensionMismatchException,
OutOfRangeException,
ConvergenceException,
MaxCountExceededException
Performs an ANOVA test, evaluating the null hypothesis that there is no difference among the means of the data categories.

Preconditions:

• The categoryData Collection must contain double[] arrays.
• There must be at least two double[] arrays in the categoryData collection and each of these arrays must contain at least two values.
• alpha must be strictly greater than 0 and less than or equal to 0.5.

This implementation uses the commons-math F Distribution implementation to estimate the exact p-value, using the formula

   p = 1 - cumulativeProbability(F)
where F is the F value and cumulativeProbability is the commons-math implementation of the F distribution.

True is returned iff the estimated p-value is less than alpha.

Parameters:
categoryData - Collection of double[] arrays each containing data for one category
alpha - significance level of the test
Returns:
true if the null hypothesis can be rejected with confidence 1 - alpha
Throws:
NullArgumentException - if categoryData is null
DimensionMismatchException - if the length of the categoryData array is less than 2 or a contained double[] array does not have at least two values
OutOfRangeException - if alpha is not in the range (0, 0.5]
ConvergenceException - if the p-value can not be computed due to a convergence error
MaxCountExceededException - if the maximum number of iterations is exceeded