Could someone please clarify why in Chi-squared and F-statistic calculation formulas sample variances are used as $s^2$ and not $s^2/n$ (like in Z or t tests)?

$\chi^2 = \frac{(n-1)s^2}{\sigma^2} $

$F = \frac{s^2_1}{s^2_2}$

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    $\begingroup$ Which formulas specifically are you asking about? Statistics with these distributions appear in many contexts and have many different formulas. $\endgroup$ – whuber Dec 1 '15 at 22:07
  • $\begingroup$ I edited the post, it should be clearer now. $\endgroup$ – vaidqs Dec 1 '15 at 22:22

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