R: Two Sample Variance Tests

varianceTest {fBasics} | R Documentation

## Two Sample Variance Tests

### Description

Tests if two series differ in their distributional variance parameter.

### Usage

    varianceTest(x, y, method = c("varf", "bartlett", "fligner"),
        title = NULL, description = NULL)

### Arguments

`x, y` | numeric vectors of data values.
`method` | a character string naming which test should be applied.
`title` | an optional title string, if not specified the inputs data name is deparsed.
`description` | optional description string, or a vector of character strings.

### Details

The `method="varf"` can be used to compare variances of two normal samples performing an F test. The null hypothesis is that the ratio of the variances of the populations from which they were drawn is equal to one.

The `method="bartlett"` performs the Bartlett test of the null hypothesis that the variances in each of the samples are the same. This fact of equal variances across samples is also called homogeneity of variances. Note, that Bartlett's test is sensitive to departures from normality. That is, if the samples come from non-normal distributions, then Bartlett's test may simply be testing for non-normality. The Levene test (not yet implemented) is an alternative to the Bartlett test that is less sensitive to departures from normality.

The `method="fligner"` performs the Fligner-Killeen test of the null that the variances in each of the two samples are the same.

### Value

In contrast to R's output report from S3 objects of class `"htest"` a different output report is produced. The classical tests presented here return an S4 object of class `"fHTEST"`. The object contains the following slots:

`@call` | the function call.
`@data` | the data as specified by the input argument(s).
`@test` | a list whose elements contain the results from the statistical test. The information provided is similar to a list object of class `"htest"`.
`@title` | a character string with the name of the test. This can be overwritten specifying a user defined input argument.
`@description` | a character string with an optional user defined description. By default just the current date when the test was applied will be returned.

The slot `@test` returns an object of class `"list"` containing (at least) the following elements:

`statistic` | the value(s) of the test statistic.
`p.value` | the p-value(s) of the test.
`parameters` | a numeric value or vector of parameters.
`estimate` | a numeric value or vector of sample estimates.
`conf.int` | a numeric two row vector or matrix of 95
`method` | a character string indicating what type of test was performed.
`data.name` | a character string giving the name(s) of the data.

### Note

Some of the test implementations are selected from R's `ctest` package.

### Author(s)

R-core team for hypothesis tests implemented from R's package `ctest`.

### References

Conover, W. J. (1971); Practical nonparametric statistics, New York: John Wiley & Sons.

Lehmann E.L. (1986); Testing Statistical Hypotheses, John Wiley and Sons, New York.

### Examples

    ## rnorm -
       # Generate Series:
       x = rnorm(50)
       y = rnorm(50)

    ## varianceTest -
       varianceTest(x, y, "varf")
       varianceTest(x, y, "bartlett")
       varianceTest(x, y, "fligner")

[Package fBasics version 3042.89 Index]