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hotellval(x [, pval:T]), REAL matrix x with no MISSING elements

Keywords: hotelling tsq, hypothesis tests
hotellval(x), where x is a n by p REAL matrix with no MISSING elements,
returns a REAL scalar containing Hotelling's T^2 statistic for testing
the null hypothesis H0:  mu = 0.  mu' is the expectation of each row of
x when the rows are assumed to be random sample from a multi-variate

It is an error if n <= p.

hotellval(x, pval:T) does the same, except a P-value is also computed
under the assumption that the rows of x are independent multivariate
normal.  The result is structure(hotelling:tsq, pvalue:pval), where tsq
and pval are REAL scalars.

  Cmd> hotellval(x - mu0', pval:T)

where mu0 is a REAL vector of length p, computes a test statistic and
associated P-value for testing H0: mu = mu0.

  Cmd> hotellval(x1 - x2, pval:T)

where x1 and x2 are both n by p, computes Hotelling's paired P^2
statistic for testing H0: E(x1 - x2) = 0, together with a P-value.

See also hotell2val(), tval() and t2val().

Gary Oehlert 2003-01-15