In statistics Hotelling's T-squared distribution is important because it arises as the distribution of a set of statistics which are natural generalisations of the statistics underlying Student's t distribution. In particular, the distribution arises in multivariate statistics in undertaking tests of the differences between the (multivariate) means of different populations, where tests for univariate problems would make use of a t-test. It is proportional to the F distribution.
The distribution is named for Harold Hotelling, who developed it as a generalization of Student's t distribution.
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“In this distribution of functions, the scholar is the delegated intellect. In the right state, he is, Man Thinking. In the degenerate state, when the victim of society, he tends to become a mere thinker, or, still worse, the parrot of other mens thinking.”
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