com.numericalmethod.suanshu.stats.test.variance
Class F

java.lang.Object
  com.numericalmethod.suanshu.stats.test.HypothesisTest
      com.numericalmethod.suanshu.stats.test.variance.F

public class F
extends HypothesisTest

The F-test tests whether two normal populations have the same variance. This test is sensitive to the assumption that the variables are normally distributed.

The R equivalent function is var.test.

See Also:

Wikipedia: FDistribution-test of equality of variances

Constructor Summary

F(double[] sample1, double[] sample2)
Perform the F-test to test for equal variance of two normal populations.

F(double[] sample1, double[] sample2, double ratio)
Perform the F-test to test for equal variance of two normal populations.

Method Summary

double[]	confidenceInterval(double confidence) Compute the confidence interval.
java.lang.String	getAlternativeHypothesis() Get the description of the alternative hypothesis.
java.lang.String	getNullHypothesis() Get a description of the null hypothesis.
double	leftConfidenceInterval(double confidence) Compute the one sided left confidence interval, [0, a]
double	leftOneSidedPvalue() Get the left, one-sided p-value.
double	pValue() Get the p-value for the test statistics.
double	rightConfidenceInterval(double confidence) Compute the one sided right confidence interval, [a, ∞)
double	rightOneSidedPvalue() Get the right, one-sided p-value.
double	statistics() Get the test statistics.

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

isNullRejected, nGroups, nObs, oneSidedPvalue

Methods inherited from class java.lang.Object

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

Constructor Detail

F

public F(double[] sample1,
         double[] sample2)

Perform the F-test to test for equal variance of two normal populations.

Parameters:

sample1 - sample 1

sample2 - sample 2

F

public F(double[] sample1,
         double[] sample2,
         double ratio)

Perform the F-test to test for equal variance of two normal populations.

Parameters:

sample1 - sample 1

sample2 - sample 2

ratio - the hypothesized ratio of the population variances of samples 1 and 2

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 the description of the alternative hypothesis.

Specified by:

getAlternativeHypothesis in class HypothesisTest

Returns:

the alternative hypothesis description

See Also:

Wikipedia: Alternative hypothesis

statistics

public double statistics()

Description copied from class: HypothesisTest

Get the test statistics.

Specified by:

statistics in class HypothesisTest

Returns:

the test statistics

See Also:

Wikipedia: Test statistic

pValue

public double pValue()

Description copied from class: HypothesisTest

Get the p-value for the test statistics.

Specified by:

pValue in class HypothesisTest

Returns:

the p-value

See Also:

Wikipedia: P-value

rightOneSidedPvalue

public double rightOneSidedPvalue()

Get the right, one-sided p-value.

Returns:

the right, one-sided p-value.

leftOneSidedPvalue

public double leftOneSidedPvalue()

Get the left, one-sided p-value.

Returns:

the left, one-sided p-value.

confidenceInterval

public double[] confidenceInterval(double confidence)

Compute the confidence interval.

Parameters:

confidence - the confidence level, e.g., for a 2-sided 95% confidence interval, we use 0.975 because 1 - 0.95 = 2 * (1 - 0.025)

Returns:

the left and right interval bounds

rightConfidenceInterval

public double rightConfidenceInterval(double confidence)

Compute the one sided right confidence interval, [a, ∞)

Parameters:

confidence - the confidence level, e.g., 0.95 for 95% confidence interval

Returns:

the left interval bound

leftConfidenceInterval

public double leftConfidenceInterval(double confidence)

Compute the one sided left confidence interval, [0, a]

Parameters:

confidence - the confidence level, e.g., 0.95 for 95% confidence interval

Returns:

the right interval bound