ChiSquare Test for One Variance and F Test to Compare Two Variances

Performs either a one sample chi-squared test to compare the variance of a vector with a given value or an F test to compare the variances of two samples from normal populations.

VarTest(x, ...)

# Default S3 method
VarTest(x, y,
        alternative = c("two.sided", "less", "greater"),
        ratio = 1, sigma.squared = 1,
        conf.level = 0.95, ...)

# S3 method for class 'formula'
VarTest(formula, data, subset, na.action, ...)

Arguments

x, y: numeric vectors of data values.
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.
ratio: the hypothesized ratio of the population variances of x and y.
sigma.squared: a number indicating the true value of the variance, if one sample test is requested.
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 matrix or data frame (or similar: see model.frame) containing the variables in the formula formula. By default the variables are taken from environment(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 NAs. Defaults to getOption("na.action").
...: further arguments to be passed to or from methods.

Details

The formula interface is only applicable for the 2-sample tests.

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 distribution 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.

Author

Andri Signorell <andri@signorell.net> (One sample test)
Two Sample test and help text from R-Core.

Examples

x <- rnorm(50, mean = 0, sd = 2)

# One sample test
VarTest(x, sigma.squared = 2.5)
#> 
#> 	One Sample Chi-Square test on variance
#> 
#> data:  x
#> X-squared = 67, df = 49, p-value = 0.07
#> alternative hypothesis: true variance is not equal to 2.5
#> 95 percent confidence interval:
#>  2.39 5.31
#> sample estimates:
#> variance of x 
#>          3.42 
#> 

# two samples
y <- rnorm(30, mean = 1, sd = 1)
VarTest(x, y)                  # Do x and y have the same variance?
#> 
#> 	F test to compare two variances
#> 
#> data:  x and y
#> F = 5, num df = 49, denom df = 29, p-value = 0.00002
#> alternative hypothesis: true ratio of variances is not equal to 1
#> 95 percent confidence interval:
#>  2.52 9.44
#> sample estimates:
#> ratio of variances 
#>               5.02 
#> 
VarTest(lm(x ~ 1), lm(y ~ 1))  # The same.
#> 
#> 	F test to compare two variances
#> 
#> data:  x and y
#> F = 5, num df = 49, denom df = 29, p-value = 0.00002
#> alternative hypothesis: true ratio of variances is not equal to 1
#> 95 percent confidence interval:
#>  2.52 9.44
#> sample estimates:
#> ratio of variances 
#>               5.02 
#>