com.numericalmethod.suanshu.stats.test

Class HypothesisTest

java.lang.Object

com.numericalmethod.suanshu.stats.test.HypothesisTest

All Implemented Interfaces:

java.io.Serializable

Direct Known Subclasses:

AugmentedDickeyFuller, Bartlett, BoxPierce, BreuschPagan, BrownForsythe, ChiSquare4Independence, DAgostino, F, FAEstimator, Glejser, HarveyGodfrey, JarqueBera, KolmogorovSmirnov, KruskalWallis, Levene, Lilliefors, OneWayANOVA, ShapiroWilk, SiegelTukey, T, VanDerWaerden, White, WilcoxonRankSum, WilcoxonSignedRank

public abstract class HypothesisTest
extends java.lang.Object
implements java.io.Serializable

A statistical hypothesis test is a method of making decisions using experimental data. A result is called statistically significant if it is unlikely to have occurred by chance.

Specifically, given a null hypothesis, we compute the p-value of a test statistics. The p-value tells the probability of observing the observations. We often accept the alternative hypothesis, (i.e. rejects a null hypothesis) if the p-value is less than 0.05 or 0.01, corresponding respectively to a 5% or 1% chance of rejecting the null hypothesis when it is true.

See Also:

• Wikipedia: Statistical hypothesis testing
• Wikipedia: Test statistic
• Wikipedia: P-value
• Wikipedia: Null hypothesis
• Wikipedia: Alternative hypothesis

, Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
int	k number of groups of observations
int	N total number of observations
protected double	pValue p-value for the test statistics
protected double	testStatistics the test statistics

Constructor Summary

Constructors

Modifier	Constructor and Description
protected	HypothesisTest(double[]... samples) Construct an instance of HypothesisTest from samples.

Method Summary

Modifier and Type	Method and Description
abstract java.lang.String	getAlternativeHypothesis() Get a description of the alternative hypothesis.
abstract java.lang.String	getNullHypothesis() Get a description of the null hypothesis.
boolean	isNullRejected(double alpha) Use p-value to check whether the null hypothesis can be rejected for given significance level (size) alpha.
static double	oneSidedPvalue(ProbabilityDistribution F, double x) A one-sided P-value is the probability of observing a test statistic at least as extreme as the one observed; hence, the one-sided P-value is simply given by the complementary cumulative distribution function (survival function) for continuous distribution.
double	pValue() Get the p-value.
double	statistics() Get the test statistics.

Methods inherited from class java.lang.Object

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

Field Detail

k

public final int k

number of groups of observations

N

public final int N

total number of observations

testStatistics

protected volatile double testStatistics

the test statistics

pValue

protected volatile double pValue

p-value for the test statistics

Constructor Detail

HypothesisTest

protected HypothesisTest(double[]... samples)

Construct an instance of HypothesisTest from samples.

Parameters:

samples - an array of samples

Method Detail

statistics

public double statistics()

Get the test statistics.

Returns:

the test statistics

See Also:

Wikipedia: Test statistic

pValue

public double pValue()

Get the p-value.

Returns:

the p-value

See Also:

Wikipedia: P-value

isNullRejected

public boolean isNullRejected(double alpha)

Use p-value to check whether the null hypothesis can be rejected for given significance level (size) alpha.

Parameters:

alpha - significance level (size) of test

Returns:

true if the hypothesis is rejected due to p-value < alpha

getNullHypothesis

public abstract java.lang.String getNullHypothesis()

Get a description of the null hypothesis.

Returns:

the null hypothesis description

See Also:

Wikipedia: Null hypothesis

getAlternativeHypothesis

public abstract java.lang.String getAlternativeHypothesis()

Get a description of the alternative hypothesis.

Returns:

the alternative hypothesis description

See Also:

Wikipedia: Alternative hypothesis

oneSidedPvalue

public static double oneSidedPvalue(ProbabilityDistribution F,
                                    double x)

A one-sided P-value is the probability of observing a test statistic at least as extreme as the one observed; hence, the one-sided P-value is simply given by the complementary cumulative distribution function (survival function) for continuous distribution.

For discrete distribution, we need to include the probability observing the critical value as well.

Parameters:

F - a univariate distribution

x - the critical value

Returns:

the p-value for the critical value