Package org.apache.commons.math.stat.inference

Class TTestImpl

java.lang.Object
org.apache.commons.math.stat.inference.TTestImpl
All Implemented Interfaces:
TTest
public class TTestImpl extends Object implements TTest
Implements t-test statistics defined in the TTest interface.

Uses commons-math TDistributionImpl implementation to estimate exact p-values.

  • Constructor Summary

    Constructors
    Constructor
    Description
    TTestImpl()
    Default constructor.
    TTestImpl(TDistribution t)
    Deprecated.
    in 2.2 (to be removed in 3.0).

  • Method Summary

    Modifier and Type
    Method
    Description
    double
    homoscedasticT(double[] sample1, double[] sample2)
    Computes a 2-sample t statistic, under the hypothesis of equal subpopulation variances.
    double
    homoscedasticT(StatisticalSummary sampleStats1, StatisticalSummary sampleStats2)
    Computes a 2-sample t statistic, comparing the means of the datasets described by two StatisticalSummary instances, under the assumption of equal subpopulation variances.
    double
    homoscedasticTTest(double[] sample1, double[] sample2)
    Returns the observed significance level, or p-value, associated with a two-sample, two-tailed t-test comparing the means of the input arrays, under the assumption that the two samples are drawn from subpopulations with equal variances.
    boolean
    homoscedasticTTest(double[] sample1, double[] sample2, double alpha)
    Performs a two-sided t-test evaluating the null hypothesis that sample1 and sample2 are drawn from populations with the same mean, with significance level alpha, assuming that the subpopulation variances are equal.
    double
    homoscedasticTTest(StatisticalSummary sampleStats1, StatisticalSummary sampleStats2)
    Returns the observed significance level, or p-value, associated with a two-sample, two-tailed t-test comparing the means of the datasets described by two StatisticalSummary instances, under the hypothesis of equal subpopulation variances.
    double
    pairedT(double[] sample1, double[] sample2)
    Computes a paired, 2-sample t-statistic based on the data in the input arrays.
    double
    pairedTTest(double[] sample1, double[] sample2)
    Returns the observed significance level, or p-value, associated with a paired, two-sample, two-tailed t-test based on the data in the input arrays.
    boolean
    pairedTTest(double[] sample1, double[] sample2, double alpha)
    Performs a paired t-test evaluating the null hypothesis that the mean of the paired differences between sample1 and sample2 is 0 in favor of the two-sided alternative that the mean paired difference is not equal to 0, with significance level alpha.
    void
    setDistribution(TDistribution value)
    Deprecated.
    in 2.2 (to be removed in 3.0).
    double
    t(double[] sample1, double[] sample2)
    Computes a 2-sample t statistic, without the hypothesis of equal subpopulation variances.
    double
    t(double mu, double[] observed)
    Computes a t statistic given observed values and a comparison constant.
    double
    t(double mu, StatisticalSummary sampleStats)
    Computes a t statistic to use in comparing the mean of the dataset described by sampleStats to mu.
    double
    t(StatisticalSummary sampleStats1, StatisticalSummary sampleStats2)
    Computes a 2-sample t statistic , comparing the means of the datasets described by two StatisticalSummary instances, without the assumption of equal subpopulation variances.
    double
    tTest(double[] sample1, double[] sample2)
    Returns the observed significance level, or p-value, associated with a two-sample, two-tailed t-test comparing the means of the input arrays.
    boolean
    tTest(double[] sample1, double[] sample2, double alpha)
    Performs a two-sided t-test evaluating the null hypothesis that sample1 and sample2 are drawn from populations with the same mean, with significance level alpha.
    double
    tTest(double mu, double[] sample)
    Returns the observed significance level, or p-value, associated with a one-sample, two-tailed t-test comparing the mean of the input array with the constant mu.
    boolean
    tTest(double mu, double[] sample, double alpha)
    Performs a two-sided t-test evaluating the null hypothesis that the mean of the population from which sample is drawn equals mu.
    double
    tTest(double mu, StatisticalSummary sampleStats)
    Returns the observed significance level, or p-value, associated with a one-sample, two-tailed t-test comparing the mean of the dataset described by sampleStats with the constant mu.
    boolean
    tTest(double mu, StatisticalSummary sampleStats, double alpha)
    Performs a two-sided t-test evaluating the null hypothesis that the mean of the population from which the dataset described by stats is drawn equals mu.
    double
    tTest(StatisticalSummary sampleStats1, StatisticalSummary sampleStats2)
    Returns the observed significance level, or p-value, associated with a two-sample, two-tailed t-test comparing the means of the datasets described by two StatisticalSummary instances.
    boolean
    tTest(StatisticalSummary sampleStats1, StatisticalSummary sampleStats2, double alpha)
    Performs a two-sided t-test evaluating the null hypothesis that sampleStats1 and sampleStats2 describe datasets drawn from populations with the same mean, with significance level alpha.

    Methods inherited from class java.lang.Object

    equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • TTestImpl

      public TTestImpl()
      Default constructor.

    • TTestImpl

      @Deprecated public TTestImpl(TDistribution t)
      Deprecated.
      in 2.2 (to be removed in 3.0).
      Create a test instance using the given distribution for computing inference statistics.
      Parameters:
      t - distribution used to compute inference statistics.
      Since:
      1.2

  • Method Details

    • pairedT

      public double pairedT(double[] sample1, double[] sample2) throws IllegalArgumentException, MathException
      Computes a paired, 2-sample t-statistic based on the data in the input arrays. The t-statistic returned is equivalent to what would be returned by computing the one-sample t-statistic t(double, double[]), with mu = 0 and the sample array consisting of the (signed) differences between corresponding entries in sample1 and sample2.

      Preconditions:

      • The input arrays must have the same length and their common length must be at least 2.

      Specified by:
      pairedT in interface TTest
      Parameters:
      sample1 - array of sample data values
      sample2 - array of sample data values
      Returns:
      t statistic
      Throws:
      IllegalArgumentException - if the precondition is not met
      MathException - if the statistic can not be computed do to a convergence or other numerical error.

    • pairedTTest

      public double pairedTTest(double[] sample1, double[] sample2) throws IllegalArgumentException, MathException
      Returns the observed significance level, or p-value, associated with a paired, two-sample, two-tailed t-test based on the data in the input arrays.

      The number returned is the smallest significance level at which one can reject the null hypothesis that the mean of the paired differences is 0 in favor of the two-sided alternative that the mean paired difference is not equal to 0. For a one-sided test, divide the returned value by 2.

      This test is equivalent to a one-sample t-test computed using tTest(double, double[]) with mu = 0 and the sample array consisting of the signed differences between corresponding elements of sample1 and sample2.

      Usage Note:
      The validity of the p-value depends on the assumptions of the parametric t-test procedure, as discussed here

      Preconditions:

      • The input array lengths must be the same and their common length must be at least 2.

      Specified by:
      pairedTTest in interface TTest
      Parameters:
      sample1 - array of sample data values
      sample2 - array of sample data values
      Returns:
      p-value for t-test
      Throws:
      IllegalArgumentException - if the precondition is not met
      MathException - if an error occurs computing the p-value

    • pairedTTest

      public boolean pairedTTest(double[] sample1, double[] sample2, double alpha) throws IllegalArgumentException, MathException
      Performs a paired t-test evaluating the null hypothesis that the mean of the paired differences between sample1 and sample2 is 0 in favor of the two-sided alternative that the mean paired difference is not equal to 0, with significance level alpha.

      Returns true iff the null hypothesis can be rejected with confidence 1 - alpha. To perform a 1-sided test, use alpha * 2

      Usage Note:
      The validity of the test depends on the assumptions of the parametric t-test procedure, as discussed here

      Preconditions:

      • The input array lengths must be the same and their common length must be at least 2.
      • 0 invalid input: '<' alpha invalid input: '<' 0.5

      Specified by:
      pairedTTest in interface TTest
      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:
      IllegalArgumentException - if the preconditions are not met
      MathException - if an error occurs performing the test

    • t

      public double t(double mu, double[] observed) throws IllegalArgumentException
      Computes a t statistic given observed values and a comparison constant.

      This statistic can be used to perform a one sample t-test for the mean.

      Preconditions:

      • The observed array length must be at least 2.

      Specified by:
      t in interface TTest
      Parameters:
      mu - comparison constant
      observed - array of values
      Returns:
      t statistic
      Throws:
      IllegalArgumentException - if input array length is less than 2

    • t

      public double t(double mu, StatisticalSummary sampleStats) throws IllegalArgumentException
      Computes a t statistic to use in comparing the mean of the dataset described by sampleStats to mu.

      This statistic can be used to perform a one sample t-test for the mean.

      Preconditions:

      • observed.getN() > = 2.

      Specified by:
      t in interface TTest
      Parameters:
      mu - comparison constant
      sampleStats - DescriptiveStatistics holding sample summary statitstics
      Returns:
      t statistic
      Throws:
      IllegalArgumentException - if the precondition is not met

    • homoscedasticT

      public double homoscedasticT(double[] sample1, double[] sample2) throws IllegalArgumentException
      Computes a 2-sample t statistic, under the hypothesis of equal subpopulation variances. To compute a t-statistic without the equal variances hypothesis, use t(double[], double[]).

      This statistic can be used to perform a (homoscedastic) two-sample t-test to compare sample means.

      The t-statisitc is

         t = (m1 - m2) / (sqrt(1/n1 +1/n2) sqrt(var))

      where n1 is the size of first sample; n2 is the size of second sample; m1 is the mean of first sample; m2 is the mean of second sample

    and var is the pooled variance estimate:

    var = sqrt(((n1 - 1)var1 + (n2 - 1)var2) / ((n1-1) + (n2-1)))

    with var1 the variance of the first sample and var2 the variance of the second sample.

    Preconditions:

    • The observed array lengths must both be at least 2.