HotellingsT2Test
Hotelling's T2 Test
Hotelling's T2 test is the multivariate generlisation of the Student's t test. A onesample Hotelling's T2 test can be used to test if a set of vectors of data (which should be a sample of a single statistical population) has a mean equal to a hypothetical mean. A twosample Hotelling's T2 test may be used to test for significant differences between the mean vectors (multivariate means) of two multivariate data sets are different.
 Keywords
 htest, multivariate
Usage
HotellingsT2Test(x, ...)
"HotellingsT2Test"(x, y = NULL, mu = NULL, test = "f", ...)
"HotellingsT2Test"(formula, data, subset, na.action, ...)
Arguments
 x
 a numeric data frame or matrix.
 y
 an optional numeric data frame or matrix for the two sample test. If
NULL
a one sample test is performed.  mu
 a vector indicating the hypothesized value of the mean (or difference
in means if a two sample test is performed).
NULL
represents origin or no difference between the groups.  test
 if
"f"
, the decision is based on the Fdistribution, if"chi"
a chisquared approximation is used.  formula
 a formula of the form
x ~ g
wherex
is a numeric matrix giving the data values andg
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 formulaformula
. By default the variables are taken fromenvironment(formula)
.  subset
 an optional vector specifying a subset of observations to be used.
 na.action
 a function which indicates what should happen when the data contain NAs. Defaults to
getOption("na.action")
.  ...
 further arguments to be passed to or from methods.
Details
The classical test for testing the location of a multivariate population or for testing the mean
difference for two multivariate populations. When test = "f"
the Fdistribution is used for
the test statistic and it is assumed that the data are normally distributed. If the chisquare
approximation is used, the normal assumption can be relaxed to existence of second moments.
In the two sample case both populations are assumed to have the same covariance matrix.
The formula interface is only applicable for the 2sample tests.
Value

A list with class 'htest' containing the following components:
References
Nordhausen K., Sirkia S., Oja H. and Tyler D. E. (2012) ICSNP: Tools for Multivariate Nonparametrics. R package version 1.09. https://cran.rproject.org/package=ICSNP
Anderson, T.W. (2003), An introduction to multivariate analysis, New Jersey: Wiley.
Examples
math.teach < data.frame(
teacher = factor(rep(1:2, c(3, 6))),
satis = c(1, 3, 2, 4, 6, 6, 5, 5, 4),
know = c(3, 7, 2, 6, 8, 8, 10, 10, 6))
with(math.teach,
HotellingsT2Test(cbind(satis, know) ~ teacher))