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'''Hotelling's T-squared distribution''' is a multivariate generalization of the [[Statistics/StudentsTDistribution|t distribution]]. '''Hotelling's T-squared distribution''' is a multivariate generalization of the [[Analysis/StudentsTDistribution|t distribution]].
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The T-squared distribution is a generalization of the [[Statistics/StudentsTDistribution|t distribution]] for multiple jointly normally distributed variables. The T-squared distribution is used for the generalization of [[Statistics/StudentsTTest|t tests]] for multiple jointly [[Analysis/NormalDistribution|normally distributed]] variables. It is in fact a scaled version of the [[Analysis/FDistribution|F distribution]].
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 * two sample means as ''x,,1,,'' and ''x,,2,,''
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Note that this is a scaled version of the [[Statistics/FDistribution|F distribution]].
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Much like how the [[Statistics/StudentsTDistribution|t distribution]] is used for [[Statistics/StudentsTTest|t tests]], this distribution is used for [[Statistics/HotellingsTSquaredTest|multivariate t tests]]. Much like how the [[Analysis/StudentsTDistribution|t distribution]] is used for [[Statistics/StudentsTTest|t tests]], this distribution is used for [[Statistics/HotellingsTSquaredTest|multivariate t tests]].

Hotelling's T-squared Distribution

Hotelling's T-squared distribution is a multivariate generalization of the t distribution.

Contents

  1. Hotelling's T-squared Distribution
    1. Description
    2. Usage
      1. Probability Tests

Description

The T-squared distribution is used for the generalization of t tests for multiple jointly normally distributed variables. It is in fact a scaled version of the F distribution.

Consider the univariate case: there are

These sample means are characterized by the t distribution with n1 + n2 - 2 degrees of freedom.

The T-squared distribution generalizes this to p variables. The distribution is notated as T2(p, n1+n2-2).

Usage

Probability Tests

Much like how the t distribution is used for t tests, this distribution is used for multivariate t tests.

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Analysis/HotellingsTSquaredDistribution (last edited 2026-02-17 15:57:41 by DominicRicottone)