gov.sandia.cognition.statistics.method

Class GaussianConfidence

java.lang.Object

gov.sandia.cognition.util.AbstractCloneableSerializable

gov.sandia.cognition.statistics.method.GaussianConfidence

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="Gaussian Z-test",
                           alsoKnownAs="Z-test",
                           description="Determines if two populations have the same mean, if the populations are Gaussian and relatively large, at least 30 or so.",
                           assumptions={"The two groups are sampled independently of each other.","The two groups are sampled from a Gaussian distribution, or the underlying distributions are non-Gaussian but obey the weak law of large numbers.","The variances of the two groups are equal."},
                           nullHypothesis="The means of the groups are equal.",
                           dataPaired=false,
                           dataSameSize=false,
                           distribution=UnivariateGaussian.CDF.class,
                           reference=@PublicationReference(author="Wikipedia",title="Z-test",type=WebPage,year=2009,url="http://en.wikipedia.org/wiki/Z-test"))
public class GaussianConfidence
extends AbstractCloneableSerializable
implements NullHypothesisEvaluator<java.util.Collection<? extends java.lang.Number>>, ConfidenceIntervalEvaluator<java.util.Collection<? extends java.lang.Number>>

This test is sometimes called the "Z test" Defines a range of values that the statistic can take, as well as the confidence that the statistic is between the lower and upper bounds. This test is useful in those situations where the tested data were generated by a (univariate) Gaussian distribution.

Since:

2.0

Author:

Kevin R. Dixon

See Also:

Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	GaussianConfidence.Statistic Confidence statistics for a Gaussian distribution

Field Summary

Fields

Modifier and Type	Field and Description
static GaussianConfidence	INSTANCE This class has no members, so here's a static instance.

Constructor Summary

Constructors

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

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
static ConfidenceInterval	computeConfidenceInterval(UnivariateDistribution<?> dataDistribution, int numSamples, double confidence) Computes the Gaussian confidence interval given a distribution of data, number of samples, and corresponding confidence interval
static GaussianConfidence.Statistic	evaluateNullHypothesis(java.util.Collection<? extends java.lang.Double> data1, double data2) Computes the probability that the input was drawn from the estimated UnivariateGaussian distribution.
GaussianConfidence.Statistic	evaluateNullHypothesis(java.util.Collection<? extends java.lang.Number> data1, java.util.Collection<? extends java.lang.Number> data2) Computes the probability that two data were generated by the same distribution.

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 GaussianConfidence INSTANCE

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

Constructor Detail

GaussianConfidence

public GaussianConfidence()

Creates a new instance of GaussianConfidence

Method Detail

evaluateNullHypothesis

public GaussianConfidence.Statistic evaluateNullHypothesis(java.util.Collection<? extends java.lang.Number> data1,
                                                           java.util.Collection<? extends java.lang.Number> data2)

Description copied from interface: NullHypothesisEvaluator

Computes the probability that two data were generated by the same distribution. NullHypothesisProbability=1 means that the distributions are likely the same, NullHypothesisProbability=0 means they are likely NOT the same, and NullHypothesisProbability less than 0.05 is the standard statistical significance test. This is the "p-value" that social scientists like to use.

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:

Probability that the two data were generated by the same source. A value of NullHypothesisProbability less than 0.05 is the standard point at which social scientists say two distributions were generated by different sources.

evaluateNullHypothesis

public static GaussianConfidence.Statistic evaluateNullHypothesis(java.util.Collection<? extends java.lang.Double> data1,
                                                                  double data2)

Computes the probability that the input was drawn from the estimated UnivariateGaussian distribution. That is, what is the probability that the UnivariateGaussian could produce a MORE UNLIKELY sample than the given "input". For example, the probability of drawing a more unlikely sample that the mean is 1.0 and infinity is 0.0

Parameters:

data1 - Dataset to consider

data2 - Sample to compute the probability that a UnivariateGaussian would produce a more unlikely sample than "data2"

Returns:

probability that the input was drawn from this estimated UnivariateGaussian distribution. That is, what is the probability that the UnivariateGaussian could produce a MORE UNLIKELY sample than the given input

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 static ConfidenceInterval computeConfidenceInterval(UnivariateDistribution<?> dataDistribution,
                                                           int numSamples,
                                                           double confidence)

Computes the Gaussian confidence interval given a distribution of data, number of samples, and corresponding confidence interval

Parameters:

dataDistribution - UnivariateGaussian describing the distribution of the underlying data

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

computeConfidenceInterval

@PublicationReference(author="Wikipedia",
                      title="Standard error (statistics)",
                      type=WebPage,
                      year=2009,
                      url="http://en.wikipedia.org/wiki/Standard_error_(statistics)")
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