R: F Test to Compare Two Variances

var.test {ctest} | R Documentation

## F Test to Compare Two Variances

### Description

Performs an F test to compare the variances of two samples from normal populations.

### Usage

    var.test(x, y, ratio = 1, alternative = c("two.sided", "less", "greater"),
             conf.level = 0.95, ...)
    var.test(formula, data, subset, na.action, ...)

### Arguments

`x, y` | numeric vectors of data values, or fitted linear model objects (inheriting from class `"lm"`).
`ratio` | the hypothesized ratio of the population variances of `x` and `y`.
`alternative` | a character string specifying the alternative hypothesis, must be one of `"two.sided"` (default), `"greater"` or `"less"`. You can specify just the initial letter.
`conf.level` | confidence level for the returned confidence interval.
`formula` | a formula of the form `lhs ~ rhs` where `lhs` is a numeric variable giving the data values and `rhs` a factor with two levels giving the corresponding groups.
`data` | an optional data frame containing the variables in the model formula.
`subset` | an optional vector specifying a subset of observations to be used.
`na.action` | a function which indicates what should happen when the data contain `NA`s. Defaults to `getOption("na.action")`.
`...` | further arguments to be passed to or from methods.

### Details

The null hypothesis is that the ratio of the variances of the populations from which `x` and `y` were drawn, or in the data to which the linear models `x` and `y` were fitted, is equal to `ratio`.

### Value

A list with class `"htest"` containing the following components:

`statistic` | the value of the F test statistic.
`parameter` | the degrees of the freedom of the F distribtion of the test statistic.
`p.value` | the p-value of the test.
`conf.int` | a confidence interval for the ratio of the population variances.
`estimate` | the ratio of the sample variances of `x` and `y`.
`null.value` | the ratio of population variances under the null.
`alternative` | a character string describing the alternative hypothesis.
`method` | the character string `"F test to compare two variances"`.
`data.name` | a character string giving the names of the data.

### See Also

`bartlett.test` for testing homogeneity of variances in more than two samples from normal distributions; `ansari.test` and `mood.test` for two rank based (nonparametric) two-sample tests for difference in scale.

### Examples

    x <- rnorm(50, mean = 0, sd = 2)
    y <- rnorm(30, mean = 1, sd = 1)
    var.test(x, y)                  # Do x and y have the same variance?
    var.test(lm(x ~ 1), lm(y ~ 1))  # The same.

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