rrcov (version 0.4-01)

T2.test: Robust Hotelling T2 test

Description

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

Usage

T2.test(x, ...)

## S3 method for class 'default':
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, \dots)

Arguments

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(for

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 NAs. Defaults to getOption("na.action") (currently only "na.rm" used)

...

further arguments to be passed to or from methods.

Value

• 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.

Details

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

References

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

See Also

CovMcd

Examples

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

## Two-sample robust 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])


T2.test(x,y, method="mcd")    ## error - not yet implemented