FisherRatioTest

Test whether the variance of a population is one:

The -values are typically large under :

The -values are typically small when is false:

Compare the variance of a population to a particular value:

Compare the variances of two populations:

The -values are typically large when the variances are equal:

The -values are typically small when the variances are not equal:

Test whether the ratio of the variances of two datasets is a particular value:

The following forms are equivalent:

The order of the datasets should be considered when determining :

Create a HypothesisTestData object for repeated property extraction:

The properties available for extraction;

Extract some properties from a HypothesisTestData object:

The -value, test statistic, and degrees of freedom:

Extract any number of properties simultaneously:

The -value, test statistic, and degrees of freedom:

Tabulate test results:

The values from the table can be extracted using :

Tabulate -values or test statistics:

The -value from the table:

The test statistic from the table:

A two-sided test is performed by default:

Test versus :

Perform a two-sided test or a one-sided alternative:

Test versus :

Test versus :

Test versus :

Perform tests with one-sided alternatives when a null value is given:

Test versus :

Test versus :

Set the significance level for diagnostic tests:

By default, is used:

The significance level is also used for and :

Diagnostics can be controlled as a group using All or None:

Verify all assumptions:

Check no assumptions:

Diagnostics can be controlled independently:

Check for normality:

It is often useful to bypass diagnostic tests for simulation purposes:

The assumptions of the test hold by design, so a great deal of time can be saved:

The results are identical:

A laboratory is considering replacing a voltage meter with one that claims to be more accurate. The makers of the new meter allowed a test run to determine its effectiveness. A lab technician measured the voltage produced by 15 power supplies set to 9 volts:

A PairedTTest shows that the readings from the two meters do not differ significantly:

A test for equal variance shows that the new meter has less error than the old meter:

The Fisher ratio test is equivalent to the LeveneTest for a single dataset:

It is also equivalent to the BrownForsytheTest for a single dataset:

Given a single dataset with length , the test statistic follows a ChiSquareDistribution under :

The maximum likelihood estimate of the degrees of freedom is near :

The test statistic for the FisherRatioTest for two samples:

Given two datasets with lengths and , the test statistic follows an FRatioDistribution under :

The Fisher ratio test is very sensitive to the assumption of normality:

The distribution of the test statistic is not a ChiSquareDistribution:

For a sample of size with sample variance from a NormalDistribution, the random variable has a ChiSquareDistribution:

The following has an FRatioDistribution:

The test statistic for the FisherRatioTest follows an FRatioDistribution:

The Fisher ratio test is only appropriate for normally distributed data:

Use the ConoverTest or the SiegelTukeyTest when the data is not normally distributed: