Given univariate samples \(X_1~,\ldots,~X_k\), it tests $$H_0 : \sigma_1^2 = \cdots \sigma_k^2\quad vs\quad H_1 : \textrm{at least one equality does not hold}$$ using the procedure by Brown and Forsythe (1974).
vark.1974BF(dlist)a list of length \(k\) where each element is a sample vector.
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.
Brown MB, Forsythe AB (1974). “Robust Tests for the Equality of Variances.” Journal of the American Statistical Association, 69(346), 364--367. ISSN 0162-1459, 1537-274X.
## CRAN-purpose small example
small1d = list()
for (i in 1:5){ # k=5 sample
small1d[[i]] = rnorm(20)
}
vark.1974BF(small1d) # run the test
#>
#> Brown-Forsythe Test for Homogeneity of Variance
#>
#> data: small1d
#> statistic = 0.98285, p-value = 0.4208
#> alternative hypothesis: at least one of equalities does not hold.
#>
# \donttest{
## test when k=5 (samples)
## empirical Type 1 error
niter = 1000
counter = rep(0,niter) # record p-values
for (i in 1:niter){
mylist = list()
for (j in 1:5){
mylist[[j]] = rnorm(50)
}
counter[i] = ifelse(vark.1974BF(mylist)$p.value < 0.05, 1, 0)
}
## print the result
cat(paste("\n* Example for 'vark.1974BF'\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 'vark.1974BF'
#> *
#> * number of rejections : 47
#> * total number of trials : 1000
#> * empirical Type 1 error : 0.047
# }