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  "body": "\n## Summary\n\nHotelling's T-squared distribution is the multivariate analogue of the square of Student's $t$-distribution.\nIt is the distribution of a squared Mahalanobis-type length $m\\, x^T M^{-1} x$ of a normal vector $x$, measured with an independent Wishart matrix $M$.\nA rescaling of it is an F-distribution.\nIt is the null distribution of Hotelling's $T^2$ test for the mean vector of a multivariate normal sample.\n\n## Explanations\n\n### L1 human\n\nTo test whether the mean of one variable is zero, one divides the sample mean by its estimated standard error and gets a $t$ statistic.\nWith several variables at once, the variables have different scales and are correlated.\nHotelling's statistic measures the distance of the sample mean vector from the hypothesized mean in units given by the sample covariance matrix.\nIts distribution, when the hypothesis holds, is Hotelling's T-squared distribution.\nWith a single variable it reduces to the square of the $t$ statistic.\n",
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