hotelling.test: Hotelling's T2 Test

hotelling.testR Documentation

Hotelling's T2 Test


Hotelling's T2 test for one and two samples.


hotelling.test(matrix1, matrix2 = NULL)



A numeric matrix or dataframe in which each row represents an observation of a multivariate random variable, and each column represents a dimension of that variable.


An optional second numeric matrix or dataframe of the same column rank as 'matrix1'.


If a single matrix is provided, this function tests the alternative hypothesis that all column means are not equal to zero. If a second matrix is provided, the alternative hypothesis to be tested is that the group means are not all equal. The statistic is tested using an F-distribution which assumes that the matrices represent (roughly) multivariate normal variables.

This function is only designed for multivariate tests of location. If a univariate test is desired, please use a t-test.


An object of class 'Hotelling.test', a list containing the elements:


The value of the test statistic.


The numerator degrees of freedom for the F statistic.


The denominator degrees of freedom for the F statistic


The p-value for the test.


The number of independent samples involved in the test.


Santiago Barreda <>


Hotelling, H. (1931). The generalization of Student's ratio. Annals of Mathematical Statistics 2 (3): 360-378.'s_T-squared_distribution


## load Peterson & Barney data
#data (pb52)

## separate the Peterson & Barney vowels by speaker
## gender and age (child vs. adult)
#men = pb52[pb52$sex == 'm' & pb52$type == 'm',]
#women = pb52[pb52$sex == 'f' & pb52$type == 'w',]
#boys = pb52[pb52$sex == 'm' & pb52$type == 'c',]
#girls = pb52[pb52$sex == 'f' & pb52$type == 'c',]

## fit 4 separate models which predict F1 frequency 
## on the basis of vowel category. 
#men = rcr (f1 ~ vowel, men$speaker, men)
#women = rcr (f1 ~ vowel, women$speaker, women)
#boys = rcr (f1 ~ vowel, boys$speaker, boys)
#girls = rcr (f1 ~ vowel, girls$speaker, girls)

## A Hotelling T2 test indicates that there are 
## significant differences in F1 frequency 
## based on vowel category between males and females
#hotelling.test (men$coefficients, women$coefficients)

## but no significant differences based on the same 
## criteria between boys and girls.
#hotelling.test (boys$coefficients, girls$coefficients)

phonTools documentation built on Nov. 21, 2023, 1:07 a.m.