To put it simply, the F-test fulfills two main tasks:
Number one, it can be utilized to check whether a calculated regression is statistically significant, that is, whether the relationship between two variables, obtained by the regression, is true not only for the sample, but also for the entire population.
Secondly, with the help of an F-test one can ascertain whether two samples of different populations differ significantly in terms of a feature in their variance.
There are two surveys being conducted in Boston and Washington D.C. about body size. The F-test will determine, whether the variance (dispersion) of body sizes in the two populations differ significantly from each other. If this is the case, it is statistically useful to consider the characteristic 'height' separately for Boston and Washington D.C. If the variance is not deviant, it is permissible to combine the two cities in respect of this characteristic.
Please note that the definitions in our statistics encyclopedia are simplified explanations of terms. Our goal is to make the definitions accessible for a broad audience; thus it is possible that some definitions do not adhere entirely to scientific standards.