Bartlett's Test for Homogeneity of Variance

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 Bartlett (1937).

vark.1937Bartlett(dlist)

Arguments

dlist: a list of length $k$ where each element is a sample vector.

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.

References

Bartlett MS (1937). “Properties of Sufficiency and Statistical Tests.” Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 160(901), 268--282. ISSN 00804630.

Examples

## CRAN-purpose small example
small1d = list()
for (i in 1:5){ # k=5 sample
  small1d[[i]] = rnorm(20)
}
vark.1937Bartlett(small1d) # run the test
#> 
#> 	Bartlett's Test for Homogeneity of Variance.
#> 
#> data:  small1d
#> statistic = 2.9006, p-value = 0.5746
#> 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.1937Bartlett(mylist)$p.value < 0.05, 1, 0)
}

## print the result
cat(paste("\n* Example for 'vark.1937Bartlett'\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.1937Bartlett'
#> *
#> * number of rejections   : 51
#> * total number of trials : 1000
#> * empirical Type 1 error : 0.051
# }