com.numericalmethod.suanshu.stats.test.distribution.normality

Class Lilliefors

java.lang.Object

com.numericalmethod.suanshu.stats.test.HypothesisTest

com.numericalmethod.suanshu.stats.test.distribution.normality.Lilliefors

All Implemented Interfaces:

java.io.Serializable

public class Lilliefors
extends HypothesisTest

Lilliefors test tests the null hypothesis that data come from a normally distributed population with an estimated sample mean and variance. The test statistic is the maximal absolute difference between empirical and the hypothetical NormalDistribution distribution function.

Since the hypothesized CDF has been moved closer to the data by estimation based on the data, the "null distribution" of the test statistic, i.e. its probability distribution assuming the null hypothesis is true, is stochastically smaller than the Kolmogorov–Smirnov distribution, hence the Lilliefors distribution.

We first compute the p-value from the Dallal-Wilkinson (1986) formula, which is claimed to be only reliable when the p-value is smaller than 0.1. When this p-value is > 0.1, we compute again the p-value from the distribution of the modified statistic (Stephen 1974).

The R equivalent function is lillie.test in package nortest.

See Also:

• Wikipedia: Lilliefors test
• Dallal, G.E. and Wilkinson, L. "An analytic approximation to the distribution of Lilliefors' test for normality," The American Statistician, 40, 294–296. 1986.
• Stephens, M.A. "EDF statistics for goodness of fit and some comparisons," Journal of the American Statistical Association, 69, 730–737. 1974.

, Serialized Form

Field Summary

Fields inherited from class com.numericalmethod.suanshu.stats.test.HypothesisTest

k, N, pValue, testStatistics

Constructor Summary

Constructors

Constructor and Description
Lilliefors(double[] sample) Perform the Lilliefors test to test for the null hypothesis that data come from a normally distributed population with an estimated sample mean and variance.

Method Summary

Modifier and Type	Method and Description
java.lang.String	getAlternativeHypothesis() Get a description of the alternative hypothesis.
java.lang.String	getNullHypothesis() Get a description of the null hypothesis.

Methods inherited from class com.numericalmethod.suanshu.stats.test.HypothesisTest

isNullRejected, oneSidedPvalue, pValue, statistics

Methods inherited from class java.lang.Object

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

Constructor Detail

Lilliefors

public Lilliefors(double[] sample)

Perform the Lilliefors test to test for the null hypothesis that data come from a normally distributed population with an estimated sample mean and variance.

Parameters:

sample - a sample

Method Detail

getNullHypothesis

public java.lang.String getNullHypothesis()

Description copied from class: HypothesisTest

Get a description of the null hypothesis.

Specified by:

getNullHypothesis in class HypothesisTest

Returns:

the null hypothesis description

See Also:

Wikipedia: Null hypothesis

getAlternativeHypothesis

public java.lang.String getAlternativeHypothesis()

Description copied from class: HypothesisTest

Get a description of the alternative hypothesis.

Specified by:

getAlternativeHypothesis in class HypothesisTest

Returns:

the alternative hypothesis description

See Also:

Wikipedia: Alternative hypothesis