# Using $\chi^2$ result to find asymptotic distribution of $S^2$ when $X_i$ normally distributed

At the end of this answer it is mentioned that

Note: the above result of course holds also for normally distributed samples -but in this last case we have also available a finite-sample chi-square distributional result.

What is this result? If possible, can someone provide an illustration (or a link/reference to an illustration) where this $\chi^2$ result is used?

• The $\chi^2$ distribution usually arises as a (multiple of a) sum of squares of zero-mean normal variables. This basic result is at the foundation of $\chi^2$ tests and F-ratio tests in ANOVA, the Student t test, and much more. You can find out more about this from, say, the Wikipedia page on the $\chi^2$ distribution or by searching our site. – whuber Jun 26 '17 at 16:39