vark.1937Bartlett {SHT}

Bartlett's Test for Homogeneity of Variance

Description

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).

Usage

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


## 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=""))