# mean2.1931Hotelling: Two-sample Hotelling's T-squared Test for Multivariate Means In SHT: Statistical Hypothesis Testing Toolbox

 mean2.1931Hotelling 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 : μ_x = μ_y\quad vs\quad H_1 : μ_x \neq μ_y

using the procedure by Hotelling (1931).

### Usage

mean2.1931Hotelling(X, Y, paired = FALSE, var.equal = TRUE)


### Arguments

 X an (n_x \times p) data matrix of 1st sample. Y an (n_y \times p) data matrix of 2nd sample. 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 under H_0.

alternative

alternative hypothesis.

method

name of the test.

data.name

name(s) of provided sample data.

### References

\insertRef

hotelling_generalization_1931SHT

### 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=""))



SHT documentation built on Nov. 3, 2022, 9:06 a.m.