mean2.1931Hotelling {SHT} | R Documentation |
Two-sample Hotelling's T-squared Test for Multivariate Means
Description
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 Hotelling (1931).
Usage
mean2.1931Hotelling(X, Y, paired = FALSE, var.equal = TRUE)
Arguments
X |
an |
Y |
an |
paired |
a logical; whether you want a paired Hotelling's test. |
var.equal |
a logical; whether to treat the two covariances as being equal. |
Value
a (list) object of S3
class htest
containing:
- statistic
a test statistic.
- p.value
p
-value underH_0
.- alternative
alternative hypothesis.
- method
name of the test.
- data.name
name(s) of provided sample data.
References
Hotelling H (1931). “The Generalization of Student's Ratio.” The Annals of Mathematical Statistics, 2(3), 360–378. ISSN 0003-4851.
Examples
## CRAN-purpose small example
smallX = matrix(rnorm(10*3),ncol=3)
smallY = matrix(rnorm(10*3),ncol=3)
mean2.1931Hotelling(smallX, smallY) # run the test
## generate two samples from standard normal distributions.
X = matrix(rnorm(50*5), ncol=5)
Y = matrix(rnorm(77*5), ncol=5)
## run single test
print(mean2.1931Hotelling(X,Y))
## empirical Type 1 error
niter = 1000
counter = rep(0,niter) # record p-values
for (i in 1:niter){
X = matrix(rnorm(50*5), ncol=5)
Y = matrix(rnorm(77*5), ncol=5)
counter[i] = ifelse(mean2.1931Hotelling(X,Y)$p.value < 0.05, 1, 0)
}
## print the result
cat(paste("\n* Example for 'mean2.1931Hotelling'\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=""))
[Package SHT version 0.1.8 Index]