# SuanShu, a Java numerical and statistical library

com.numericalmethod.suanshu.stats.test.variance

## Class 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.

Wikipedia: FDistribution-test of equality of variances
• ### Constructor Summary

Constructors
Constructor and Description
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

All Methods
Modifier and Type Method and Description
double[] confidenceInterval(double confidence)
Compute the confidence interval.
String getAlternativeHypothesis()
Get the description of the alternative hypothesis.
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 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
Wikipedia: Null hypothesis
• #### getAlternativeHypothesis

public 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
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
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
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