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

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 population. 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. Examples: 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