Given two multivariate data \(X\) and \(Y\) of same dimension, it tests $$H_0 : \mu_x = \mu_y\quad vs\quad H_1 : \mu_x \neq \mu_y$$ using the procedure by Yao (1965) via multivariate modification of Welch's approximation of degrees of freedoms.
mean2.1965Yao(X, Y)an \((n_x \times p)\) data matrix of 1st sample.
an \((n_y \times p)\) data matrix of 2nd sample.
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.
Yao Y (1965). “An Approximate Degrees of Freedom Solution to the Multivariate Behrens Fisher Problem.” Biometrika, 52(1/2), 139. ISSN 00063444.
## CRAN-purpose small example
smallX = matrix(rnorm(10*3),ncol=3)
smallY = matrix(rnorm(10*3),ncol=3)
mean2.1965Yao(smallX, smallY) # run the test
#>
#> Two-sample Test for Multivariate Means by Yao (1965).
#>
#> data: smallX and smallY
#> T2 = 5.3858, p-value = 0.241
#> alternative hypothesis: true means are different.
#>
# \donttest{
## empirical Type 1 error
niter = 1000
counter = rep(0,niter) # record p-values
for (i in 1:niter){
X = matrix(rnorm(50*5), ncol=10)
Y = matrix(rnorm(50*5), ncol=10)
counter[i] = ifelse(mean2.1965Yao(X,Y)$p.value < 0.05, 1, 0)
}
## print the result
cat(paste("\n* Example for 'mean2.1965Yao'\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 'mean2.1965Yao'
#> *
#> * number of rejections : 50
#> * total number of trials : 1000
#> * empirical Type 1 error : 0.05
# }