var.test
F Test to Compare Two Variances

### Description

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

### Usage

    var.test(x, ...)
    ## Default S3 method:
    var.test(x, y, ratio = 1, alternative = c("two.sided", "less", "greater"),
        conf.level = 0.95, ...)
    ## S3 method for class 'formula':
    var.test(formula, data, subset, na.action, ...)

### Arguments

x, y | numeric vectors or objects of class lm that contain the sample values. Missing values (NAs) and infinite values (Infs) are ignored.
ratio | a positive numeric value that specifies the ratio of the two variances.
alternative | a character string that specifies the alternative hypothesis. alternative refers to the true population variance for x in relation to that for y. Options are: "two.sided" the true ratio of variances of x and y is not equal to ratio. "greater" the true ratio of variances of x and y is greater than ratio. "less" the true ratio of variances of x and y is less than ratio. You need enter only enough of the character string to create a unique match.
conf.level | a numeric vector in the range [0, 1] that specifies the confidence level for the returned confidence interval.
formula | a formula of the form v~g that gives the name of a numeric variable (v) and the name of a grouping factor (g). g must have exactly two levels and length equal to that of v.
data | a data frame that contains the variables named in the formula and subset arguments. Defaults to the parent frame from which the function was called.
subset | a vector that specifies which subset of the rows of the data should be used. This can be a logical vector that is replicated to have length equal to the number of rows of data, a numeric vector that indicates the row numbers to be included, or a character vector of the row names that should be included. By default, all rows are included.
na.action | a function that handles missing values. See na.action for details.
... | additional arguments.

### Details

Methods

var.test | The generic method.
var.test.formula | The S3 method implemented for the class formula.
var.test.default | The default S3 method.

Null hypothesis
The null hypothesis states that the population variances are equal. The alternative hypothesis states that the variance of the population from which x is drawn is greater than, less than, or simply not equal to the variance of the population from which y is drawn. Use the alternative input argument to specify the alternative hypothesis.
Test assumptions
The var.test function relies on the assumption that the input vectors x and y were drawn from normal populations. Outliers have a relatively strong influence on the variance estimates and may have a significant effect on the results.
Value
returns a list of class htest that contains the following components:

statistic | F-statistic with names attribute "F". The value is calculated using the formula:
(var(x)/var(y)) / ratio
parameter | degrees of freedom (vector of length 2) of the F-distribution that is associated with statistic along with the names attribute c("num df", "denom df").
p.value | p-value for the test.
conf.int | confidence interval (vector of length 2) for the ratio of the true population variance of x to y. The confidence level is specified in the conf.level argument.
estimate | the ratio of the sample variances as calculated by var(x)/var(y) along with the names attribute "ratio of variances".
null.value | the ratio of population variances specified by the null hypothesis along with the names attribute "ratio of variances".
alternative | a character string that returns the alternative hypothesis (two.sided, greater, or less) as specified in the alternative argument.
method | a character string for the name of the method used for the calculation.
data.name | a character string (vector of length 1) that contains the names of the x and y input vectors.

References
Box, G. E. P., Hunter, W. G. and Hunter, J. S. (1978). Statistics for Experimenters. New York: Wiley.
Snedecor, G. W. and Cochran, W. G. (1980). Statistical Methods, 7th ed. Ames, Iowa: Iowa State University Press.
See Also
var, F
Examples

    # The null hypothesis is that 'x' and 'y' come from
    # populations with the same variance. These populations
    # are assumed to be normal. The alternative hypothesis is
    # that the population variances are not equal. The
    # confidence interval for the ratio of the population
    # variances will have a confidence level of 0.90.
    x <- rnorm(22)
    y <- rnorm(20,0,1.5)
    var.test(x, y, conf.level=.9)
    # The null hypothesis is as above. The alternative
    # hypothesis is that the population variance for
    # 'x' is greater than that for 'y'.
    var.test(x, y, alternative = "greater")
    var.test(lm(x ~ 1), lm(y ~ 1))  # The same as var.test(x, y)
    # Formula interface - large vs small cars, exclude sporty cars
    var.test(Mileage ~ I(Type
        data=Sdatasets::fuel.frame, subset = (Type != "Sporty"))

Package stats version 6.1.5-18
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