gov.sandia.cognition.statistics.method

Class StudentTConfidence

java.lang.Object

gov.sandia.cognition.util.AbstractCloneableSerializable

gov.sandia.cognition.statistics.method.StudentTConfidence

All Implemented Interfaces:

ConfidenceIntervalEvaluator<java.util.Collection<? extends java.lang.Number>>, NullHypothesisEvaluator<java.util.Collection<? extends java.lang.Number>>, CloneableSerializable, java.io.Serializable, java.lang.Cloneable

@ConfidenceTestAssumptions(name="Paired Student\'s t-test",
                           description="Computes the value of the null hypothesis that the differences between paired samples have zero mean and that the data are sampled from a Gaussian distributions with equal variances.",
                           alsoKnownAs="Dependent t-test for paired samples",
                           nullHypothesis="The means of the groups are equal.",
                           assumptions={"The data for the pairs are iid samples from a Gaussian distribution with equal variances.","The common variances times the degrees of freedom is a chi-square distribution.","The data pairs should be sampled independently from each other."},
                           distribution=StudentTDistribution.CDF.class,
                           dataPaired=true,
                           dataSameSize=true,
                           reference=@PublicationReference(author="Wikipedia",title="Student\'s t-test, Dependent t-test for paired samples",type=WebPage,year=2009,url="http://en.wikipedia.org/wiki/Student_t_test#Dependent_t-test_for_paired_samples"))
public class StudentTConfidence
extends AbstractCloneableSerializable
implements NullHypothesisEvaluator<java.util.Collection<? extends java.lang.Number>>, ConfidenceIntervalEvaluator<java.util.Collection<? extends java.lang.Number>>

This class implements Student's t-tests for different uses. The confidence test is the Paired Student's t-test to determine if the difference between the pairs have zero mean. The confidence interval calculation computes the Student-t confidence interval for the mean of the given data.

Since:

2.0

Author:

Kevin R. Dixon

See Also:

Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	StudentTConfidence.Statistic Confidence statistics for a Student-t test
static class	StudentTConfidence.Summary An implementation of the Summarizer interface for creating a ConfidenceInterval

Field Summary

Fields

Modifier and Type	Field and Description
static double	DEFAULT_TOLERANCE Default tolerance for the standard deviation, 1.0E-10.
static StudentTConfidence	INSTANCE This class has no members, so here's a static instance.

Constructor Summary

Constructors

Constructor and Description
StudentTConfidence() Creates a new instance of StudentTConfidence

Method Summary

Modifier and Type	Method and Description
ConfidenceInterval	computeConfidenceInterval(java.util.Collection<? extends java.lang.Number> data, double confidence) Computes a confidence interval for a given dataset and confidence (power) level
ConfidenceInterval	computeConfidenceInterval(double mean, double variance, int numSamples, double confidence) Computes the confidence interval given the mean and variance of the samples, number of samples, and corresponding confidence interval
StudentTConfidence.Statistic	evaluateNullHypothesis(java.util.Collection<? extends java.lang.Number> data1, java.util.Collection<? extends java.lang.Number> data2) Computes a paired Student-t test for the given data.

Methods inherited from class gov.sandia.cognition.util.AbstractCloneableSerializable

clone

Methods inherited from class java.lang.Object

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

Methods inherited from interface gov.sandia.cognition.util.CloneableSerializable

clone

Field Detail

INSTANCE

public static final StudentTConfidence INSTANCE

This class has no members, so here's a static instance.

DEFAULT_TOLERANCE

public static final double DEFAULT_TOLERANCE

Default tolerance for the standard deviation, 1.0E-10.

See Also:

Constant Field Values

Constructor Detail

StudentTConfidence

public StudentTConfidence()

Creates a new instance of StudentTConfidence

Method Detail

evaluateNullHypothesis

@PublicationReference(author={"William H. Press","Saul A. Teukolsky","William T. Vetterling","Brian P. Flannery"},
                      title="Numerical Recipes in C, Second Edition",
                      type=Book,
                      year=1992,
                      pages=618,
                      notes="Function tptest()",
                      url="http://www.nrbook.com/a/bookcpdf.php")
public StudentTConfidence.Statistic evaluateNullHypothesis(java.util.Collection<? extends java.lang.Number> data1,
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          java.util.Collection<? extends java.lang.Number> data2)

Computes a paired Student-t test for the given data. The datasets must be the same size.

Specified by:

evaluateNullHypothesis in interface NullHypothesisEvaluator<java.util.Collection<? extends java.lang.Number>>

Parameters:

data1 - First dataset to consider

data2 - Second dataset to consider

Returns:

ConfidenceStatistic for a Student-t test

computeConfidenceInterval

public ConfidenceInterval computeConfidenceInterval(java.util.Collection<? extends java.lang.Number> data,
                                                    double confidence)

Description copied from interface: ConfidenceIntervalEvaluator

Computes a confidence interval for a given dataset and confidence (power) level

Specified by:

computeConfidenceInterval in interface ConfidenceIntervalEvaluator<java.util.Collection<? extends java.lang.Number>>

Parameters:

data - Dataset to use to compute the ConfidenceInterval

confidence - Confidence level (power, 1-pvalue) for the ConfidenceInterval, must be on the interval (0,1]

Returns:

ConfidenceInterval describing the range of values that contain the estimate for the given confidence level

computeConfidenceInterval

public ConfidenceInterval computeConfidenceInterval(double mean,
                                                    double variance,
                                                    int numSamples,
                                                    double confidence)

Description copied from interface: ConfidenceIntervalEvaluator

Computes the confidence interval given the mean and variance of the samples, number of samples, and corresponding confidence interval

Specified by:

computeConfidenceInterval in interface ConfidenceIntervalEvaluator<java.util.Collection<? extends java.lang.Number>>

Parameters:

mean - Mean of the distribution.

variance - Variance of the distribution.

numSamples - Number of samples in the underlying data

confidence - Confidence value to assume for the ConfidenceInterval

Returns:

ConfidenceInterval capturing the range of the mean of the data at the desired level of confidence