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Hotelling T2


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A statistic having a multivariate distribution which is the analogue of the univariate t-distribution. The statistic was introduced in 1931 by Hotelling. A sample of size n is drawn from a multivariate normal distribution with mean vector μ and variance–covariance matrix estimated as S. If the column vector of sample means is denoted by the statistic T2 is given by

T2=n(μ)′S−1(μ).

For p×1 vectors, {(np)T2}/{(n−1)p} has an F-distribution with p and (np) degrees of freedom. See also Mahalanobis D2.

Subjects: Probability and Statistics.


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