# hotelling.test: Hotelling's T2 Test In phonTools: Tools for Phonetic and Acoustic Analyses

## Description

Hotelling's T2 test for one and two samples.

## Usage

 `1` ```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 <sbarreda@ucdavis.edu>

## 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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25``` ```## 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) ```

### Example output

``` "21.6551279985494 10 50"

Hotelling's Two-Sample T2-test
Alternative hypothesis: Group means are not all equal.

f =  21.65513 , df1 =  10 , df2 =  50 , p.value =  7.327472e-15

 "2.76324878982235 10 4"

Hotelling's Two-Sample T2-test
Alternative hypothesis: Group means are not all equal.

f =  2.763249 , df1 =  10 , df2 =  4 , p.value =  0.1697232
```

phonTools documentation built on May 1, 2019, 6:26 p.m.