SHT (version 0.1.9)

meank.2009ZX: Test for Equality of Means by Zhang and Xu (2009)

Description

Given univariate samples \(X_1~,\ldots,~X_k\), it tests $$H_0 : \mu_1 = \cdots \mu_k\quad vs\quad H_1 : \textrm{at least one equality does not hold}$$ using the procedure by Zhang and Xu (2009) by applying multivariate extension of Scheffe's method of transformation.

Usage

meank.2009ZX(dlist, method = c("L", "T"))

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

dlist

a list of length \(k\) where each element is a sample matrix of same dimension.

method

a method to be applied for the transformed problem. "L" for \(L^2\)-norm based method, and "T" for Hotelling's test, which might fail due to dimensionality. Case insensitive.

References

zhang_ksample_2009SHT

Examples

## CRAN-purpose small example
tinylist = list()
for (i in 1:3){ # consider 3-sample case
  tinylist[[i]] = matrix(rnorm(10*3),ncol=3)
}
meank.2009ZX(tinylist) # run the test

# \donttest{
## test when k=5 samples with (n,p) = (100,20)
## 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]] = matrix(rnorm(100*10),ncol=10)
  }
  
  counter[i] = ifelse(meank.2009ZX(mylist, method="L")$p.value < 0.05, 1, 0)
}

## print the result
cat(paste("\n* Example for 'meank.2009ZX'\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=""))
# }