Hotelling's T2 Test
Hotelling's T2 test is the multivariate generlisation of the Student's t test. A one-sample 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 two-sample 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.
HotellingsT2Test(x, ...)"HotellingsT2Test"(x, y = NULL, mu = NULL, test = "f", ...)"HotellingsT2Test"(formula, data, subset, na.action, ...)
- a numeric data frame or matrix.
- an optional numeric data frame or matrix for the two sample test. If
NULLa one sample test is performed.
- a vector indicating the hypothesized value of the mean (or difference
in means if a two sample test is performed).
NULLrepresents origin or no difference between the groups.
"f", the decision is based on the F-distribution, if
"chi"a chi-squared approximation is used.
- a formula of the form
x ~ gwhere
xis a numeric matrix giving the data values and
ga factor with two levels giving the corresponding groups.
- 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
- an optional vector specifying a subset of observations to be used.
- a function which indicates what should happen when the data contain NAs. Defaults to
- further arguments to be passed to or from methods.
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 F-distribution 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 2-sample tests.
A list with class 'htest' containing the following components:
Nordhausen K., Sirkia S., Oja H. and Tyler D. E. (2012) ICSNP: Tools for Multivariate Nonparametrics. R package version 1.0-9. https://cran.r-project.org/package=ICSNP
Anderson, T.W. (2003), An introduction to multivariate analysis, New Jersey: Wiley.
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))