# Why do chi-squared and F statistic formulas involve $s^2$ not $s^2/n$?

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)?

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

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

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