= Hotelling's T-squared Distribution = '''Hotelling's T-squared distribution''' is a multivariate generalization of the [[Analysis/StudentsTDistribution|t distribution]]. <> ---- == Description == 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]]. Consider the univariate case: there are * two samples of size ''n,,1,,'' and ''n,,2,,'' * a [[Statistics/PooledVariance|pooled variance]] as ''s^2^''. These sample means are characterized by the t distribution with ''n,,1,, + n,,2,, - 2'' degrees of freedom. The T-squared distribution generalizes this to ''p'' variables. The distribution is notated as ''T^2^(p, n,,1,,+n,,2,,-2)''. ---- == Usage == === Probability 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]]. ---- CategoryRicottone