Given two univariate samples \(x\) and \(y\), it tests $$H_0 : \sigma_x^2 \left\lbrace =,\geq,\leq \right\rbrace \sigma_y^2\quad vs\quad H_1 : \sigma_x^2 \left\lbrace \neq,<,>\right\rbrace \sigma_y^2$$.
var2.F(x, y, alternative = c("two.sided", "less", "greater"))a length-\(n\) data vector.
a length-\(m\) data vector.
specifying the alternative hypothesis.
a (list) object of S3 class htest containing:
a test statistic.
\(p\)-value under \(H_0\).
alternative hypothesis.
name of the test.
name(s) of provided sample data.
Snedecor GW, Cochran WG (1996). Statistical methods, 8 ed., 7. print edition. Iowa State Univ. Press, Ames, Iowa. ISBN 978-0-8138-1561-9.
## CRAN-purpose small example
x = rnorm(10)
y = rnorm(10)
var2.F(x, y, alternative="g") ## Ha : var(x) >= var(y)
#>
#> Two-Sample F Test for Variance.
#>
#> data: x and y
#> statistic = 1.5631, p-value = 0.2581
#> alternative hypothesis: true variance of x is greater than true variance of y.
#>
var2.F(x, y, alternative="l") ## Ha : var(x) <= var(y)
#>
#> Two-Sample F Test for Variance.
#>
#> data: x and y
#> statistic = 1.5631, p-value = 0.7419
#> alternative hypothesis: true variance of x is smaller than true variance of y.
#>
var2.F(x, y, alternative="t") ## Ha : var(x) =/= var(y)
#>
#> Two-Sample F Test for Variance.
#>
#> data: x and y
#> statistic = 1.5631, p-value = 0.5163
#> alternative hypothesis: two true variances are different.
#>
# \donttest{
## empirical Type 1 error
niter = 1000
counter = rep(0,niter) # record p-values
for (i in 1:niter){
x = rnorm(57) # sample x from N(0,1)
y = rnorm(89) # sample y from N(0,1)
counter[i] = ifelse(var2.F(x,y)$p.value < 0.05, 1, 0)
}
## print the result
cat(paste("\n* Example for 'var2.F'\n","*\n",
"* number of rejections : ", sum(counter),"\n",
"* total number of trials : ", niter,"\n",
"* empirical Type 1 error : ",round(sum(counter/niter),5),"\n",sep=""))
#>
#> * Example for 'var2.F'
#> *
#> * number of rejections : 48
#> * total number of trials : 1000
#> * empirical Type 1 error : 0.048
# }