hotelling.test: Two-sample Hotelling's T-squared test
In Hotelling: Hotelling's T^2 Test and Variants

Description Usage Arguments Value Methods (by class) Author(s) References See Also Examples

View source: R/hotelling.test.r

Performs a two-sample Hotelling's T-squared test for the difference in two multivariate means

hotelling.test(x, ...)

## Default S3 method:
hotelling.test(
  x,
  y,
  shrinkage = FALSE,
  var.equal = TRUE,
  perm = FALSE,
  B = 10000,
  progBar = (perm && TRUE),
  ...
)

## S3 method for class 'formula'
hotelling.test(x, data = NULL, pair = c(1, 2), ...)

`x`	a matrix containing the data points from sample 1, or a formula specifying the elements to be used as a response and the grouping variable as a predictor, or a list containing elements `mean`, `cov`, and `n` where `mean` is a mean vector of length p, `cov` is a variance-covariance matrix of dimension p by p, and `n` is the sample size
`...`	any additional arguments. This is useful to pass the optional arguments for the default call from the formula version
`y`	a matrix containing the data points from sample 2, or a list containing elements `mean`, `cov`, and `n` where `mean` is a mean vector of length p, `cov` is a variance-covariance matrix of dimension p by p, and `n` is the sample size
`shrinkage`	if `TRUE` then Shaefer and Strimmer's James-Stein shrinkage estimator is used to calculate the sample covariance matrices
`var.equal`	set to `TRUE` if the covariance matrices are (assumed to be) equal
`perm`	if `TRUE` then permutation testing is used to estimate the non-parametric P-value for the hypothesis test
`B`	if perm is TRUE, then B is the number of permutations to perform
`progBar`	if `TRUE` and `perm` is TRUE then a progress bar will be displayed whilst the permutation procedure is carried out
`data`	a data frame needs to be specified if a formula is to be used to perform the test
`pair`	a vector of length two which can be used when the grouping factor has more than two levels to select different pairs of groups. For example for a 3-level factor, pairs could be set to `c(1,3)` to perform Hotelling's test between groups 1 an 3

A list (which is also of class 'hotelling.test') with the following elements:

`stats`	a list containing all of the output from `hotelling.stat`
`pval`	the P-value from the test
`results`	if `perm == TRUE`, then all of the permuation test statisics are stored in results

default: Two-sample Hotelling's T-squared test
formula: Two-sample Hotelling's T-squared test

James M. Curran

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

Schaefer, J., and K. Strimmer (2005). “A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics.” Statist. Appl. Genet. Mol. Biol. 4: 32.

Opgen-Rhein, R., and K. Strimmer (2007). “Accurate ranking of differentially expressed genes by a distribution-free shrinkage approach.” Statist. Appl. Genet. Mol. Biol. 6: 9.

Campbell, G.P. and J. M. Curran (2009). “The interpretation of elemental composition measurements from forensic glass evidence III.” Science and Justice, 49(1),2-7.

hotelling.stat

data(container.df)
fit = hotelling.test(.~gp, data = container.df)
fit

subs.df = container.df[1:10,]
subs.df$gp = rep(1:2, c(5,5))
fitPerm = hotelling.test(Al+Fe~gp, data  = subs.df, perm =  TRUE)
fitPerm
plot(fitPerm)

data(bottle.df)
fit12 = hotelling.test(.~Number, data = bottle.df)
fit12

fit23 = hotelling.test(.~Number, data = bottle.df, pair = c(2,3))
fit23

data(manova1.df)
fit = hotelling.test(wratr+wrata~treatment, data = manova1.df, var.equal = FALSE)
fit

x = list(mean = c(7.81, 108.77, 44.92),
         cov = matrix(c(0.461, 1.18, 4.49,
                        1.18, 3776.4, -17.35, 
                        4.49, -17.35, 147.24), nc = 3, byrow = TRUE),
         n = 13)
y = list(mean = c(5.89, 41.9, 20.8),
         cov = matrix(c(0.148, -0.679, 0.209, 
                       -0.679, 96.10, 20.20,
                        0.209, 20.20, 24.18), nc = 3, byrow = TRUE),
         n = 10)
fit = hotelling.test(x, y, var.equal = FALSE)
fit