Hotelling’s T 2 Statistic
摘要
The univariate t statistic is well-known to most data analysts. If a random sample of n observations is taken from a normal distribution with mean μ and variance σ 2, the form of the statistic is given by \(\displaystyle { t = \frac {{\overline x - \mu }}{{s/\sqrt n }}, } \) where \(\overline x\) is the sample mean and s is the sample standard deviation. This statistic has a Student t-distribution with ( n − 1) degrees of freedom. Squaring the statistic, we obtain \(\displaystyle {t^2} = (\overline x - \mu ){({s^2})^{ - 1}}(\overline x - \mu ). \)