What is F-ratio?

The F-ratio is a statistical ratio which arises as the ratio of two chi-square distributions.

If X and Y are two random variables which are independent and approximately normally distributed, then their variances have chi-squared distributions. The ration of these chi-square distributions, appropriately scaled, is called the F-ratio.


The F-ratio is used extensively in analysis of variance to determine what proportion of the variation in the dependent variable is explained by an explanatory variable (and the model being tested).