SHT (version 0.1.9)

var2.F: Two-Sample F-Test for Variance

Description

Given two univariate samples \(x\) and \(y\), it tests $$H_0 : \sigma_x^2 \left\lbrace =,\geq,\leq \right\rbrace \sigma_y^2\quad vs\quad H_1 : \sigma_x^2 \left\lbrace \neq,<,>\right\rbrace \sigma_y^2$$.

Usage

var2.F(x, y, alternative = c("two.sided", "less", "greater"))

Value

a (list) object of S3 class htest containing:

statistic

a test statistic.

p.value

\(p\)-value under \(H_0\).

alternative

alternative hypothesis.

method

name of the test.

data.name

name(s) of provided sample data.

Arguments

x

a length-\(n\) data vector.

y

a length-\(m\) data vector.

alternative

specifying the alternative hypothesis.

References

snedecor_statistical_1996SHT

Examples

## CRAN-purpose small example
x = rnorm(10)
y = rnorm(10)
var2.F(x, y, alternative="g") ## Ha : var(x) >= var(y)
var2.F(x, y, alternative="l") ## Ha : var(x) <= var(y)
var2.F(x, y, alternative="t") ## Ha : var(x) =/= var(y)

# \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=""))
# }