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An F statistic is a value you get when you run an ANOVA test or a regression analysis to find out if the means between two populations are significantly different.
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Reconciling F-statistic derived in two different ways
Background: in the full-rank model let $\mathbf{b}$ be a $p\times 1$ matrix of independent standard normal random variables and $\mathbf{X}$ a $n\times p$ matrix where $\mathbf{y} = \mathbf{Xb} + \mat …