T2.test: Robust Hotelling T2 test
In armstrtw/rrcov: Scalable Robust Estimators with High Breakdown Point

Description Usage Arguments Details Value Author(s) References See Also Examples

Performs one and two sample Hotelling T2 tests as well as robust one-sample Hotelling T2 test

T2.test(x, ...)

## Default S3 method:
T2.test(x, y = NULL, mu = 0, conf.level = 0.95, method=c("c", "mcd"), ...)

## S3 method for class 'formula'
T2.test(formula, data, subset, na.action, ...)

`x`	a (non-empty) numeric data frame or matrix.
`y`	an optional (non-empty) numeric data frame or matrix.
`mu`	an optional (non-empty) numeric vector of data values (or a single number which will be repeated p times) indicating the true value of the mean (or difference in means if you are performing a two sample test).
`conf.level`	confidence level of the interval
`method`	the method to be used - 'c' for sample mean and covariance matrix and 'mcd' for minimum covariance determinant estimator. A two-sample MCD based T2-test is not yet implemented.
`formula`	a formula of the form `lhs ~ rhs` where `lhs` is a numeric data frame or matrix giving the observations and `rhs` a factor with two levels giving the corresponding groups.
`data`	an optional matrix or data frame (or similar: see `model.frame`) containing the variables in the formula `formula`. By default the variables are taken from `environment(formula)`.
`subset`	an optional vector specifying a subset of observations to be used (currently not used)
`na.action`	a function which indicates what should happen when the data contain `NA`s. Defaults to `getOption("na.action")` (currently only "na.rm" used)
`...`	further arguments to be passed to or from methods.

The formula interface is only applicable for the two-sample tests.

A list with class "htest" containing the following components:

`statistic`	the value of the T2-statistic.
`parameter`	the degrees of freedom for the T2-statistic.
`p.value`	the p-value for the test.
`conf.int`	a confidence interval for the mean vector appropriate to the specified alternative hypothesis.
`estimate`	the estimated mean vector or vectors depending on whether it was a one-sample test or a two-sample test.
`null.value`	the specified hypothesized value of the mean or mean difference depending on whether it was a one-sample test or a two-sample test.
`alternative`	a character string describing the alternative hypothesis.
`method`	a character string indicating what type of T2-test was performed.
`data.name`	a character string giving the name(s) of the data.

Valentin Todorov valentin.todorov@chello.at

Willems G., Pison G., Rousseeuw P. and Van Aelst S. (2002), A robust hotelling test, Metrika, 55, 125–138.

CovMcd

## One-sample classical test
data(delivery)
delivery.x <- delivery[,1:2]
T2.test(delivery.x)

## One-sample robust test
data(delivery)
delivery.x <- delivery[,1:2]
T2.test(delivery.x, method="mcd")

## Two-sample classical test
data(hemophilia)
grp <-as.factor(hemophilia[,3])
x <- hemophilia[which(grp==levels(grp)[1]),1:2]
y <- hemophilia[which(grp==levels(grp)[2]),1:2]
T2.test(x,y)

## or using the formula interface
T2.test(as.matrix(hemophilia[,-3])~hemophilia[,3])


## Not run: 
## Two-sample robust test
T2.test(x,y, method="mcd")    ## error - not yet implemented

## End(Not run)