phonTools (version 0.1-6)

hotelling.test: 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'.

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.

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.

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',]

## 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)