hotelling.test: Hotelling's T2 Test

In santiagobarreda/phonTools: Tools for Phonetic and Acoustic Analyses

Hotelling's T2 Test

Description

Hotelling's T2 test for one and two samples.

Usage

hotelling.test(matrix1, matrix2 = NULL)

Arguments

matrix1	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.
matrix2	An optional second numeric matrix or dataframe of the same column rank as 'matrix1'.

Details

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.

Value

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

f.value	The value of the test statistic.
df1	The numerator degrees of freedom for the F statistic.
df2	The denominator degrees of freedom for the F statistic
p.value	The p-value for the test.
samples	The number of independent samples involved in the test.

Author(s)

Santiago Barreda <[e-mail]>

References

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

http://en.wikipedia.org/wiki/Hotelling's_T-squared_distribution

Examples

## 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',]

santiagobarreda/phonTools documentation built on March 4, 2024, 11:13 p.m.