mean1.1931Hotelling: One-sample Hotelling's T-squared Test for Multivariate Mean

In kisungyou/SHT: Statistical Hypothesis Testing Toolbox

One-sample Hotelling's T-squared Test for Multivariate Mean

Description

Given a multivariate sample X and hypothesized mean \mu_0, it tests

H_0 : \mu_x = \mu_0\quad vs\quad H_1 : \mu_x \neq \mu_0

using the procedure by Hotelling (1931).

Usage

mean1.1931Hotelling(X, mu0 = rep(0, ncol(X)))

Arguments

X	an (n\times p) data matrix where each row is an observation.
mu0	a length-p mean vector of interest.

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)
mean1.1931Hotelling(smallX) # run the test

## Not run: 
## 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)
  counter[i] = ifelse(mean1.1931Hotelling(X)$p.value < 0.05, 1, 0)
}

## print the result
cat(paste("\n* Example for 'mean1.1931Hotelling'\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=""))

## End(Not run)

kisungyou/SHT documentation built on Feb. 27, 2025, 6:12 a.m.