I am fairly new to statistics, and during practice, i used this link between Chi-squared and F-statistics where F equals to ration between 2 Chi squared distributions. Can someone elaborate more on this relationship so that I can intuitively understand it?

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    $\begingroup$ Could you elaborate on what you're looking for? The $F$ distribution naturally emerges as the ratio of independent (scaled) chi-squared distributions and therefore often is defined that way. What more is there to explain and what kind of "intuition" is needed? $\endgroup$ – whuber Dec 4 '17 at 19:01
  • $\begingroup$ Okay so basically i take it as defined that way and use it further on? Thanks $\endgroup$ – Nemanja Boskovic Dec 4 '17 at 20:51
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    $\begingroup$ I'm not trying to suggest the question is invalid--I'm just trying to get it formulated in a way that readers will know what definition you want to start from and what kind of intuition you are looking for. For instance, one common interpretation of ANOVA (which uses the F distribution in an essential way) is that it compares within-group variances to between-group variances, so I imagine the distribution must have an interpretation in those terms. But F distributions also show up in other circumstances where such an interpretation would not apply--whence the desire for more guidance from you. $\endgroup$ – whuber Dec 4 '17 at 20:58

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