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 Schott (2007). It can be considered as a generalization
of two-sample testing procedure proposed by Bai and Saranadasa (1996).
meank.2007Schott(dlist)a list of length \(k\) where each element is a sample matrix of same dimension.
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.
Schott JR (2007). “Some high-dimensional tests for a one-way MANOVA.” Journal of Multivariate Analysis, 98(9), 1825--1839. ISSN 0047259X.
## CRAN-purpose small example
tinylist = list()
for (i in 1:3){ # consider 3-sample case
tinylist[[i]] = matrix(rnorm(10*3),ncol=3)
}
meank.2007Schott(tinylist)
#>
#> Test for Equality of Means by Schott (2007)
#>
#> data: tinylist
#> Tnp = -0.22213, p-value = 0.7516
#> alternative hypothesis: one of equalities does not hold.
#>
# \donttest{
## test when k=5 samples with (n,p) = (10,50)
## 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(10*5),ncol=5)
}
counter[i] = ifelse(meank.2007Schott(mylist)$p.value < 0.05, 1, 0)
}
## print the result
cat(paste("\n* Example for 'meank.2007Schott'\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 'meank.2007Schott'
#> *
#> * number of rejections : 24
#> * total number of trials : 1000
#> * empirical Type 1 error : 0.024
# }