InferenceTestUtils (VirtualDataSet API)

java.lang.Object
- org.apache.commons.math4.stat.inference.InferenceTestUtils

```
public class InferenceTestUtils
extends java.lang.Object
```
A collection of static methods to create inference test instances or to perform inference tests.

Since:

1.1

Method Summary

Modifier and Type	Method	Description
`static double`	`approximateP(double d, int n, int m)`
`static double`	`chiSquare(double[] expected, long[] observed)`
`static double`	`chiSquare(long[][] counts)`
`static double`	`chiSquareDataSetsComparison(long[] observed1, long[] observed2)`
`static double`	`chiSquareTest(double[] expected, long[] observed)`
`static boolean`	`chiSquareTest(double[] expected, long[] observed, double alpha)`
`static double`	`chiSquareTest(long[][] counts)`
`static boolean`	`chiSquareTest(long[][] counts, double alpha)`
`static double`	`chiSquareTestDataSetsComparison(long[] observed1, long[] observed2)`
`static boolean`	`chiSquareTestDataSetsComparison(long[] observed1, long[] observed2, double alpha)`
`static double`	`exactP(double d, int m, int n, boolean strict)`
`static double`	`g(double[] expected, long[] observed)`
`static double`	`gDataSetsComparison(long[] observed1, long[] observed2)`
`static double`	`gTest(double[] expected, long[] observed)`
`static boolean`	`gTest(double[] expected, long[] observed, double alpha)`
`static double`	`gTestDataSetsComparison(long[] observed1, long[] observed2)`
`static boolean`	`gTestDataSetsComparison(long[] observed1, long[] observed2, double alpha)`
`static double`	`gTestIntrinsic(double[] expected, long[] observed)`
`static double`	`homoscedasticT(double[] sample1, double[] sample2)`
`static double`	`homoscedasticT(StatisticalSummary sampleStats1, StatisticalSummary sampleStats2)`
`static double`	`homoscedasticTTest(double[] sample1, double[] sample2)`
`static boolean`	`homoscedasticTTest(double[] sample1, double[] sample2, double alpha)`
`static double`	`homoscedasticTTest(StatisticalSummary sampleStats1, StatisticalSummary sampleStats2)`
`static double`	`kolmogorovSmirnovStatistic(double[] x, double[] y)`
`static double`	`kolmogorovSmirnovStatistic(ContinuousDistribution dist, double[] data)`
`static double`	`kolmogorovSmirnovTest(double[] x, double[] y)`
`static double`	`kolmogorovSmirnovTest(double[] x, double[] y, boolean strict)`
`static double`	`kolmogorovSmirnovTest(ContinuousDistribution dist, double[] data)`
`static double`	`kolmogorovSmirnovTest(ContinuousDistribution dist, double[] data, boolean strict)`
`static boolean`	`kolmogorovSmirnovTest(ContinuousDistribution dist, double[] data, double alpha)`
`static double`	`monteCarloP(double d, int n, int m, boolean strict, int iterations, UniformRandomProvider rng)`
`static double`	`oneWayAnovaFValue(java.util.Collection<double[]> categoryData)`
`static double`	`oneWayAnovaPValue(java.util.Collection<double[]> categoryData)`
`static boolean`	`oneWayAnovaTest(java.util.Collection<double[]> categoryData, double alpha)`
`static double`	`pairedT(double[] sample1, double[] sample2)`
`static double`	`pairedTTest(double[] sample1, double[] sample2)`
`static boolean`	`pairedTTest(double[] sample1, double[] sample2, double alpha)`
`static double`	`rootLogLikelihoodRatio(long k11, long k12, long k21, long k22)`
`static double`	`t(double[] sample1, double[] sample2)`
`static double`	`t(double mu, double[] observed)`
`static double`	`t(double mu, StatisticalSummary sampleStats)`
`static double`	`t(StatisticalSummary sampleStats1, StatisticalSummary sampleStats2)`
`static double`	`tTest(double[] sample1, double[] sample2)`
`static boolean`	`tTest(double[] sample1, double[] sample2, double alpha)`
`static double`	`tTest(double mu, double[] sample)`
`static boolean`	`tTest(double mu, double[] sample, double alpha)`
`static double`	`tTest(double mu, StatisticalSummary sampleStats)`
`static boolean`	`tTest(double mu, StatisticalSummary sampleStats, double alpha)`
`static double`	`tTest(StatisticalSummary sampleStats1, StatisticalSummary sampleStats2)`
`static boolean`	`tTest(StatisticalSummary sampleStats1, StatisticalSummary sampleStats2, double alpha)`

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

Method Detail

homoscedasticT

public static double homoscedasticT(double[] sample1,
                                    double[] sample2)
                             throws NullArgumentException,
                                    NumberIsTooSmallException

Parameters:: sample1 - array of sample data values; sample2 - array of sample data values
Returns:: t statistic
Throws:: NullArgumentException; NumberIsTooSmallException
See Also:: TTest.homoscedasticT(double[], double[])

homoscedasticT
```
public static double homoscedasticT(StatisticalSummary sampleStats1,
                                    StatisticalSummary sampleStats2)
                             throws NullArgumentException,
                                    NumberIsTooSmallException
```
Parameters:

sampleStats1 - StatisticalSummary describing data from the first sample

sampleStats2 - StatisticalSummary describing data from the second sample

Returns:

t statistic

Throws:

NullArgumentException

NumberIsTooSmallException

See Also:

TTest.homoscedasticT(org.apache.commons.math4.stat.descriptive.StatisticalSummary, org.apache.commons.math4.stat.descriptive.StatisticalSummary)

homoscedasticTTest

public static boolean homoscedasticTTest(double[] sample1,
                                         double[] sample2,
                                         double alpha)
                                  throws NullArgumentException,
                                         NumberIsTooSmallException,
                                         OutOfRangeException,
                                         MaxCountExceededException

Parameters:: sample1 - array of sample data values; sample2 - array of sample data values; alpha - significance level of the test
Returns:: true if the null hypothesis can be rejected with confidence 1 - alpha
Throws:: NullArgumentException; NumberIsTooSmallException; OutOfRangeException; MaxCountExceededException
See Also:: TTest.homoscedasticTTest(double[], double[], double)

homoscedasticTTest

public static double homoscedasticTTest(double[] sample1,
                                        double[] sample2)
                                 throws NullArgumentException,
                                        NumberIsTooSmallException,
                                        MaxCountExceededException

Parameters:: sample1 - array of sample data values; sample2 - array of sample data values
Returns:: p-value for t-test
Throws:: NullArgumentException; NumberIsTooSmallException; MaxCountExceededException
See Also:: TTest.homoscedasticTTest(double[], double[])

homoscedasticTTest

public static double homoscedasticTTest(StatisticalSummary sampleStats1,
                                        StatisticalSummary sampleStats2)
                                 throws NullArgumentException,
                                        NumberIsTooSmallException,
                                        MaxCountExceededException

Parameters:: sampleStats1 - StatisticalSummary describing data from the first sample; sampleStats2 - StatisticalSummary describing data from the second sample
Returns:: p-value for t-test
Throws:: NullArgumentException; NumberIsTooSmallException; MaxCountExceededException
See Also:: TTest.homoscedasticTTest(org.apache.commons.math4.stat.descriptive.StatisticalSummary, org.apache.commons.math4.stat.descriptive.StatisticalSummary)

pairedT

public static double pairedT(double[] sample1,
                             double[] sample2)
                      throws NullArgumentException,
                             NoDataException,
                             DimensionMismatchException,
                             NumberIsTooSmallException

Parameters:: sample1 - array of sample data values; sample2 - array of sample data values
Returns:: t statistic
Throws:: NullArgumentException; NoDataException; DimensionMismatchException; NumberIsTooSmallException
See Also:: TTest.pairedT(double[], double[])

pairedTTest

public static boolean pairedTTest(double[] sample1,
                                  double[] sample2,
                                  double alpha)
                           throws NullArgumentException,
                                  NoDataException,
                                  DimensionMismatchException,
                                  NumberIsTooSmallException,
                                  OutOfRangeException,
                                  MaxCountExceededException

Parameters:: sample1 - array of sample data values; sample2 - array of sample data values; alpha - significance level of the test
Returns:: true if the null hypothesis can be rejected with confidence 1 - alpha
Throws:: NullArgumentException; NoDataException; DimensionMismatchException; NumberIsTooSmallException; OutOfRangeException; MaxCountExceededException
See Also:: TTest.pairedTTest(double[], double[], double)

pairedTTest

public static double pairedTTest(double[] sample1,
                                 double[] sample2)
                          throws NullArgumentException,
                                 NoDataException,
                                 DimensionMismatchException,
                                 NumberIsTooSmallException,
                                 MaxCountExceededException

Parameters:: sample1 - array of sample data values; sample2 - array of sample data values
Returns:: p-value for t-test
Throws:: NullArgumentException; NoDataException; DimensionMismatchException; NumberIsTooSmallException; MaxCountExceededException
See Also:: TTest.pairedTTest(double[], double[])

t

public static double t(double mu,
                       double[] observed)
                throws NullArgumentException,
                       NumberIsTooSmallException

Parameters:: mu - comparison constant; observed - array of values
Returns:: t statistic
Throws:: NullArgumentException; NumberIsTooSmallException
See Also:: TTest.t(double, double[])

t
```
public static double t(double mu,
                       StatisticalSummary sampleStats)
                throws NullArgumentException,
                       NumberIsTooSmallException
```
Parameters:

mu - comparison constant

sampleStats - DescriptiveStatistics holding sample summary statitstics

Returns:

t statistic

Throws:

NullArgumentException

NumberIsTooSmallException

See Also:

TTest.t(double, org.apache.commons.math4.stat.descriptive.StatisticalSummary)

t

public static double t(double[] sample1,
                       double[] sample2)
                throws NullArgumentException,
                       NumberIsTooSmallException

Parameters:: sample1 - array of sample data values; sample2 - array of sample data values
Returns:: t statistic
Throws:: NullArgumentException; NumberIsTooSmallException
See Also:: TTest.t(double[], double[])

t
```
public static double t(StatisticalSummary sampleStats1,
                       StatisticalSummary sampleStats2)
                throws NullArgumentException,
                       NumberIsTooSmallException
```
Parameters:

sampleStats1 - StatisticalSummary describing data from the first sample

sampleStats2 - StatisticalSummary describing data from the second sample

Returns:

t statistic

Throws:

NullArgumentException

NumberIsTooSmallException

See Also:

TTest.t(org.apache.commons.math4.stat.descriptive.StatisticalSummary, org.apache.commons.math4.stat.descriptive.StatisticalSummary)

tTest

public static boolean tTest(double mu,
                            double[] sample,
                            double alpha)
                     throws NullArgumentException,
                            NumberIsTooSmallException,
                            OutOfRangeException,
                            MaxCountExceededException

Parameters:: mu - constant value to compare sample mean against; sample - array of sample data values; alpha - significance level of the test
Returns:: p-value
Throws:: NullArgumentException; NumberIsTooSmallException; OutOfRangeException; MaxCountExceededException
See Also:: TTest.tTest(double, double[], double)

tTest

public static double tTest(double mu,
                           double[] sample)
                    throws NullArgumentException,
                           NumberIsTooSmallException,
                           MaxCountExceededException

Parameters:: mu - constant value to compare sample mean against; sample - array of sample data values
Returns:: p-value
Throws:: NullArgumentException; NumberIsTooSmallException; MaxCountExceededException
See Also:: TTest.tTest(double, double[])

tTest

public static boolean tTest(double mu,
                            StatisticalSummary sampleStats,
                            double alpha)
                     throws NullArgumentException,
                            NumberIsTooSmallException,
                            OutOfRangeException,
                            MaxCountExceededException

Parameters:: mu - constant value to compare sample mean against; sampleStats - StatisticalSummary describing sample data values; alpha - significance level of the test
Returns:: p-value
Throws:: NullArgumentException; NumberIsTooSmallException; OutOfRangeException; MaxCountExceededException
See Also:: TTest.tTest(double, org.apache.commons.math4.stat.descriptive.StatisticalSummary, double)

tTest

public static double tTest(double mu,
                           StatisticalSummary sampleStats)
                    throws NullArgumentException,
                           NumberIsTooSmallException,
                           MaxCountExceededException

Parameters:: mu - constant value to compare sample mean against; sampleStats - StatisticalSummary describing sample data
Returns:: p-value
Throws:: NullArgumentException; NumberIsTooSmallException; MaxCountExceededException
See Also:: TTest.tTest(double, org.apache.commons.math4.stat.descriptive.StatisticalSummary)

tTest

public static boolean tTest(double[] sample1,
                            double[] sample2,
                            double alpha)
                     throws NullArgumentException,
                            NumberIsTooSmallException,
                            OutOfRangeException,
                            MaxCountExceededException

Parameters:: sample1 - array of sample data values; sample2 - array of sample data values; alpha - significance level of the test
Returns:: true if the null hypothesis can be rejected with confidence 1 - alpha
Throws:: NullArgumentException; NumberIsTooSmallException; OutOfRangeException; MaxCountExceededException
See Also:: TTest.tTest(double[], double[], double)

tTest

public static double tTest(double[] sample1,
                           double[] sample2)
                    throws NullArgumentException,
                           NumberIsTooSmallException,
                           MaxCountExceededException

Parameters:: sample1 - array of sample data values; sample2 - array of sample data values
Returns:: p-value for t-test
Throws:: NullArgumentException; NumberIsTooSmallException; MaxCountExceededException
See Also:: TTest.tTest(double[], double[])

tTest
```
public static boolean tTest(StatisticalSummary sampleStats1,
                            StatisticalSummary sampleStats2,
                            double alpha)
                     throws NullArgumentException,
                            NumberIsTooSmallException,
                            OutOfRangeException,
                            MaxCountExceededException
```
Parameters:

sampleStats1 - StatisticalSummary describing sample data values

sampleStats2 - StatisticalSummary describing sample data values

alpha - significance level of the test

Returns:

true if the null hypothesis can be rejected with confidence 1 - alpha

Throws:

NullArgumentException

NumberIsTooSmallException

OutOfRangeException

MaxCountExceededException

See Also:

TTest.tTest(org.apache.commons.math4.stat.descriptive.StatisticalSummary, org.apache.commons.math4.stat.descriptive.StatisticalSummary, double)

tTest
```
public static double tTest(StatisticalSummary sampleStats1,
                           StatisticalSummary sampleStats2)
                    throws NullArgumentException,
                           NumberIsTooSmallException,
                           MaxCountExceededException
```
Parameters:

sampleStats1 - StatisticalSummary describing data from the first sample

sampleStats2 - StatisticalSummary describing data from the second sample

Returns:

p-value for t-test

Throws:

NullArgumentException

NumberIsTooSmallException

MaxCountExceededException

See Also:

TTest.tTest(org.apache.commons.math4.stat.descriptive.StatisticalSummary, org.apache.commons.math4.stat.descriptive.StatisticalSummary)

chiSquare

public static double chiSquare(double[] expected,
                               long[] observed)
                        throws NotPositiveException,
                               NotStrictlyPositiveException,
                               DimensionMismatchException

Parameters:: observed - array of observed frequency counts; expected - array of expected frequency counts
Returns:: chiSquare test statistic
Throws:: NotPositiveException; NotStrictlyPositiveException; DimensionMismatchException
See Also:: ChiSquareTest.chiSquare(double[], long[])

chiSquare

public static double chiSquare(long[][] counts)
                        throws NullArgumentException,
                               NotPositiveException,
                               DimensionMismatchException

Parameters:: counts - array representation of 2-way table
Returns:: chiSquare test statistic
Throws:: NullArgumentException; NotPositiveException; DimensionMismatchException
See Also:: ChiSquareTest.chiSquare(long[][])

chiSquareTest

public static boolean chiSquareTest(double[] expected,
                                    long[] observed,
                                    double alpha)
                             throws NotPositiveException,
                                    NotStrictlyPositiveException,
                                    DimensionMismatchException,
                                    OutOfRangeException,
                                    MaxCountExceededException

Parameters:: observed - array of observed frequency counts; expected - array of expected frequency counts; alpha - significance level of the test
Returns:: true iff null hypothesis can be rejected with confidence 1 - alpha
Throws:: NotPositiveException; NotStrictlyPositiveException; DimensionMismatchException; OutOfRangeException; MaxCountExceededException
See Also:: ChiSquareTest.chiSquareTest(double[], long[], double)

chiSquareTest

public static double chiSquareTest(double[] expected,
                                   long[] observed)
                            throws NotPositiveException,
                                   NotStrictlyPositiveException,
                                   DimensionMismatchException,
                                   MaxCountExceededException

Parameters:: observed - array of observed frequency counts; expected - array of expected frequency counts
Returns:: p-value
Throws:: NotPositiveException; NotStrictlyPositiveException; DimensionMismatchException; MaxCountExceededException
See Also:: ChiSquareTest.chiSquareTest(double[], long[])

chiSquareTest

public static boolean chiSquareTest(long[][] counts,
                                    double alpha)
                             throws NullArgumentException,
                                    DimensionMismatchException,
                                    NotPositiveException,
                                    OutOfRangeException,
                                    MaxCountExceededException

Parameters:: counts - array representation of 2-way table; alpha - significance level of the test
Returns:: true iff null hypothesis can be rejected with confidence 1 - alpha
Throws:: NullArgumentException; DimensionMismatchException; NotPositiveException; OutOfRangeException; MaxCountExceededException
See Also:: ChiSquareTest.chiSquareTest(long[][], double)

chiSquareTest

public static double chiSquareTest(long[][] counts)
                            throws NullArgumentException,
                                   DimensionMismatchException,
                                   NotPositiveException,
                                   MaxCountExceededException

Parameters:: counts - array representation of 2-way table
Returns:: p-value
Throws:: NullArgumentException; DimensionMismatchException; NotPositiveException; MaxCountExceededException
See Also:: ChiSquareTest.chiSquareTest(long[][])

chiSquareDataSetsComparison

public static double chiSquareDataSetsComparison(long[] observed1,
                                                 long[] observed2)
                                          throws DimensionMismatchException,
                                                 NotPositiveException,
                                                 ZeroException

Parameters:: observed1 - array of observed frequency counts of the first data set; observed2 - array of observed frequency counts of the second data set
Returns:: chiSquare test statistic
Throws:: DimensionMismatchException; NotPositiveException; ZeroException
Since:: 1.2
See Also:: ChiSquareTest.chiSquareDataSetsComparison(long[], long[])

chiSquareTestDataSetsComparison

public static double chiSquareTestDataSetsComparison(long[] observed1,
                                                     long[] observed2)
                                              throws DimensionMismatchException,
                                                     NotPositiveException,
                                                     ZeroException,
                                                     MaxCountExceededException

Parameters:: observed1 - array of observed frequency counts of the first data set; observed2 - array of observed frequency counts of the second data set
Returns:: p-value
Throws:: DimensionMismatchException; NotPositiveException; ZeroException; MaxCountExceededException
Since:: 1.2
See Also:: ChiSquareTest.chiSquareTestDataSetsComparison(long[], long[])

chiSquareTestDataSetsComparison

public static boolean chiSquareTestDataSetsComparison(long[] observed1,
                                                      long[] observed2,
                                                      double alpha)
                                               throws DimensionMismatchException,
                                                      NotPositiveException,
                                                      ZeroException,
                                                      OutOfRangeException,
                                                      MaxCountExceededException

Parameters:: observed1 - array of observed frequency counts of the first data set; observed2 - array of observed frequency counts of the second data set; alpha - significance level of the test
Returns:: true iff null hypothesis can be rejected with confidence 1 - alpha
Throws:: DimensionMismatchException; NotPositiveException; ZeroException; OutOfRangeException; MaxCountExceededException
Since:: 1.2
See Also:: ChiSquareTest.chiSquareTestDataSetsComparison(long[], long[], double)

oneWayAnovaFValue

public static double oneWayAnovaFValue(java.util.Collection<double[]> categoryData)
                                throws NullArgumentException,
                                       DimensionMismatchException

Parameters:: categoryData - Collection of double[] arrays each containing data for one category
Returns:: Fvalue
Throws:: NullArgumentException; DimensionMismatchException
Since:: 1.2
See Also:: OneWayAnova.anovaFValue(Collection)

oneWayAnovaPValue

public static double oneWayAnovaPValue(java.util.Collection<double[]> categoryData)
                                throws NullArgumentException,
                                       DimensionMismatchException,
                                       ConvergenceException,
                                       MaxCountExceededException

Parameters:: categoryData - Collection of double[] arrays each containing data for one category
Returns:: Pvalue
Throws:: NullArgumentException; DimensionMismatchException; ConvergenceException; MaxCountExceededException
Since:: 1.2
See Also:: OneWayAnova.anovaPValue(Collection)

oneWayAnovaTest

public static boolean oneWayAnovaTest(java.util.Collection<double[]> categoryData,
                                      double alpha)
                               throws NullArgumentException,
                                      DimensionMismatchException,
                                      OutOfRangeException,
                                      ConvergenceException,
                                      MaxCountExceededException

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; DimensionMismatchException; OutOfRangeException; ConvergenceException; MaxCountExceededException
Since:: 1.2
See Also:: OneWayAnova.anovaTest(Collection,double)

g

public static double g(double[] expected,
                       long[] observed)
                throws NotPositiveException,
                       NotStrictlyPositiveException,
                       DimensionMismatchException

Parameters:: observed - array of observed frequency counts; expected - array of expected frequency counts
Returns:: G-Test statistic
Throws:: NotPositiveException; NotStrictlyPositiveException; DimensionMismatchException
Since:: 3.1
See Also:: GTest.g(double[], long[])

gTest

public static double gTest(double[] expected,
                           long[] observed)
                    throws NotPositiveException,
                           NotStrictlyPositiveException,
                           DimensionMismatchException,
                           MaxCountExceededException

Parameters:: observed - array of observed frequency counts; expected - array of expected frequency counts
Returns:: p-value
Throws:: NotPositiveException; NotStrictlyPositiveException; DimensionMismatchException; MaxCountExceededException
Since:: 3.1
See Also:: GTest.gTest( double[], long[] )

gTestIntrinsic

public static double gTestIntrinsic(double[] expected,
                                    long[] observed)
                             throws NotPositiveException,
                                    NotStrictlyPositiveException,
                                    DimensionMismatchException,
                                    MaxCountExceededException

Parameters:: observed - array of observed frequency counts; expected - array of expected frequency counts
Returns:: p-value
Throws:: NotPositiveException; NotStrictlyPositiveException; DimensionMismatchException; MaxCountExceededException
Since:: 3.1
See Also:: GTest.gTestIntrinsic(double[], long[] )

gTest

public static boolean gTest(double[] expected,
                            long[] observed,
                            double alpha)
                     throws NotPositiveException,
                            NotStrictlyPositiveException,
                            DimensionMismatchException,
                            OutOfRangeException,
                            MaxCountExceededException

Parameters:: observed - array of observed frequency counts; expected - array of expected frequency counts; alpha - significance level of the test
Returns:: true iff null hypothesis can be rejected with confidence 1 - alpha
Throws:: NotPositiveException; NotStrictlyPositiveException; DimensionMismatchException; OutOfRangeException; MaxCountExceededException
Since:: 3.1
See Also:: GTest.gTest( double[],long[],double)

gDataSetsComparison

public static double gDataSetsComparison(long[] observed1,
                                         long[] observed2)
                                  throws DimensionMismatchException,
                                         NotPositiveException,
                                         ZeroException

Parameters:: observed1 - array of observed frequency counts of the first data set; observed2 - array of observed frequency counts of the second data set
Returns:: G-Test statistic
Throws:: DimensionMismatchException; NotPositiveException; ZeroException
Since:: 3.1
See Also:: GTest.gDataSetsComparison(long[], long[])

rootLogLikelihoodRatio
```
public static double rootLogLikelihoodRatio(long k11,
                                            long k12,
                                            long k21,
                                            long k22)
                                     throws DimensionMismatchException,
                                            NotPositiveException,
                                            ZeroException
```
Parameters:

k11 - number of times the two events occurred together (AB)

k12 - number of times the second event occurred WITHOUT the first event (notA,B)

k21 - number of times the first event occurred WITHOUT the second event (A, notB)

k22 - number of times something else occurred (i.e. was neither of these events (notA, notB)

Returns:

root log-likelihood ratio

Throws:

DimensionMismatchException

NotPositiveException

ZeroException

Since:

3.1

See Also:

GTest.rootLogLikelihoodRatio(long, long, long, long)

gTestDataSetsComparison

public static double gTestDataSetsComparison(long[] observed1,
                                             long[] observed2)
                                      throws DimensionMismatchException,
                                             NotPositiveException,
                                             ZeroException,
                                             MaxCountExceededException

Parameters:: observed1 - array of observed frequency counts of the first data set; observed2 - array of observed frequency counts of the second data set
Returns:: p-value
Throws:: DimensionMismatchException; NotPositiveException; ZeroException; MaxCountExceededException
Since:: 3.1
See Also:: GTest.gTestDataSetsComparison(long[], long[])

gTestDataSetsComparison

public static boolean gTestDataSetsComparison(long[] observed1,
                                              long[] observed2,
                                              double alpha)
                                       throws DimensionMismatchException,
                                              NotPositiveException,
                                              ZeroException,
                                              OutOfRangeException,
                                              MaxCountExceededException

Parameters:: observed1 - array of observed frequency counts of the first data set; observed2 - array of observed frequency counts of the second data set; alpha - significance level of the test
Returns:: true iff null hypothesis can be rejected with confidence 1 - alpha
Throws:: DimensionMismatchException; NotPositiveException; ZeroException; OutOfRangeException; MaxCountExceededException
Since:: 3.1
See Also:: GTest.gTestDataSetsComparison(long[],long[],double)

kolmogorovSmirnovStatistic

public static double kolmogorovSmirnovStatistic(ContinuousDistribution dist,
                                                double[] data)
                                         throws InsufficientDataException,
                                                NullArgumentException

Parameters:: dist - reference distribution; data - sample being evaluated
Returns:: Kolmogorov-Smirnov statistic \(D_n\)
Throws:: InsufficientDataException; NullArgumentException
Since:: 3.3
See Also:: KolmogorovSmirnovTest.kolmogorovSmirnovStatistic(ContinuousDistribution, double[])

kolmogorovSmirnovTest
```
public static double kolmogorovSmirnovTest(ContinuousDistribution dist,
                                           double[] data)
                                    throws InsufficientDataException,
                                           NullArgumentException
```
Parameters:

dist - reference distribution

data - sample being being evaluated

Returns:

the p-value associated with the null hypothesis that data is a sample from distribution

Throws:

InsufficientDataException

NullArgumentException

Since:

3.3

See Also:

KolmogorovSmirnovTest.kolmogorovSmirnovTest(ContinuousDistribution, double[])

kolmogorovSmirnovTest
```
public static double kolmogorovSmirnovTest(ContinuousDistribution dist,
                                           double[] data,
                                           boolean strict)
                                    throws InsufficientDataException,
                                           NullArgumentException
```
Parameters:

dist - reference distribution

data - sample being being evaluated

strict - whether or not to force exact computation of the p-value

Returns:

the p-value associated with the null hypothesis that data is a sample from distribution

Throws:

InsufficientDataException

NullArgumentException

Since:

3.3

See Also:

KolmogorovSmirnovTest.kolmogorovSmirnovTest(ContinuousDistribution, double[], boolean)

kolmogorovSmirnovTest
```
public static boolean kolmogorovSmirnovTest(ContinuousDistribution dist,
                                            double[] data,
                                            double alpha)
                                     throws InsufficientDataException,
                                            NullArgumentException
```
Parameters:

dist - reference distribution

data - sample being being evaluated

alpha - significance level of the test

Returns:

true iff the null hypothesis that data is a sample from distribution can be rejected with confidence 1 - alpha

Throws:

InsufficientDataException

NullArgumentException

Since:

3.3

See Also:

KolmogorovSmirnovTest.kolmogorovSmirnovTest(ContinuousDistribution, double[], double)

kolmogorovSmirnovStatistic
```
public static double kolmogorovSmirnovStatistic(double[] x,
                                                double[] y)
                                         throws InsufficientDataException,
                                                NullArgumentException
```
Parameters:

x - first sample

y - second sample

Returns:

test statistic \(D_{n,m}\) used to evaluate the null hypothesis that x and y represent samples from the same underlying distribution

Throws:

InsufficientDataException

NullArgumentException

Since:

3.3

See Also:

KolmogorovSmirnovTest.kolmogorovSmirnovStatistic(double[], double[])

kolmogorovSmirnovTest
```
public static double kolmogorovSmirnovTest(double[] x,
                                           double[] y)
                                    throws InsufficientDataException,
                                           NullArgumentException
```
Parameters:

x - first sample dataset

y - second sample dataset

Returns:

p-value associated with the null hypothesis that x and y represent samples from the same distribution

Throws:

InsufficientDataException

NullArgumentException

Since:

3.3

See Also:

KolmogorovSmirnovTest.kolmogorovSmirnovTest(double[], double[])

kolmogorovSmirnovTest
```
public static double kolmogorovSmirnovTest(double[] x,
                                           double[] y,
                                           boolean strict)
                                    throws InsufficientDataException,
                                           NullArgumentException
```
Parameters:

x - first sample dataset.

y - second sample dataset.

strict - whether or not the probability to compute is expressed as a strict inequality (ignored for large samples).

Returns:

p-value associated with the null hypothesis that x and y represent samples from the same distribution.

Throws:

InsufficientDataException

NullArgumentException

Since:

3.3

See Also:

KolmogorovSmirnovTest.kolmogorovSmirnovTest(double[], double[], boolean)

exactP
```
public static double exactP(double d,
                            int m,
                            int n,
                            boolean strict)
```
Parameters:

d - D-statistic value

n - first sample size

m - second sample size

strict - whether or not the probability to compute is expressed as a strict inequality

Returns:

probability that a randomly selected m-n partition of m + n generates \(D_{n,m}\) greater than (resp. greater than or equal to) d

Since:

3.3

See Also:

KolmogorovSmirnovTest.exactP(double, int, int, boolean)

approximateP
```
public static double approximateP(double d,
                                  int n,
                                  int m)
```
Parameters:

d - D-statistic value

n - first sample size

m - second sample size

Returns:

approximate probability that a randomly selected m-n partition of m + n generates \(D_{n,m}\) greater than d

Since:

3.3

See Also:

KolmogorovSmirnovTest.approximateP(double, int, int)

monteCarloP
```
public static double monteCarloP(double d,
                                 int n,
                                 int m,
                                 boolean strict,
                                 int iterations,
                                 UniformRandomProvider rng)
```
Parameters:

d - D-statistic value

n - first sample size

m - second sample size

iterations - number of random partitions to generate

strict - whether or not the probability to compute is expressed as a strict inequality

rng - RNG used for generating the partitions.

Returns:

proportion of randomly generated m-n partitions of m + n that result in \(D_{n,m}\) greater than (resp. greater than or equal to) d

Since:

3.3

See Also:

KolmogorovSmirnovTest.monteCarloP(double,int,int,boolean,int,UniformRandomProvider)

Class InferenceTestUtils

Method Summary

Methods inherited from class java.lang.Object

Method Detail

homoscedasticT

homoscedasticT

homoscedasticTTest

homoscedasticTTest

homoscedasticTTest

pairedT

pairedTTest

pairedTTest

t

t

t

t

tTest

tTest

tTest

tTest

tTest

tTest

tTest

tTest

chiSquare

chiSquare

chiSquareTest

chiSquareTest

chiSquareTest

chiSquareTest

chiSquareDataSetsComparison

chiSquareTestDataSetsComparison

chiSquareTestDataSetsComparison

oneWayAnovaFValue

oneWayAnovaPValue

oneWayAnovaTest

g

gTest

gTestIntrinsic

gTest

gDataSetsComparison

rootLogLikelihoodRatio

gTestDataSetsComparison

gTestDataSetsComparison

kolmogorovSmirnovStatistic

kolmogorovSmirnovTest

kolmogorovSmirnovTest

kolmogorovSmirnovTest

kolmogorovSmirnovStatistic

kolmogorovSmirnovTest

kolmogorovSmirnovTest

exactP

approximateP

monteCarloP