# The F-test is a test for variance so why do we use F-test in ANOVA? [duplicate]

To test the mean vector we use ANOVA, and to test two variances we use the F-test, but my question is in ANOVA why we do use the F-test ?

Our goal is to define an estimable quantity that will take on a known value (here 1 or close to 1) if the null hypothesis is true. By taking the ratio of sum of squares over degrees of freedom, we create an F distributed statistic. This is because given $$X_1 \sim \chi^2_{df1}, \,\,X_2 \sim \chi^2_{df2}$$ $$Y =\frac{X_1/df1}{X_2/df2}$$ Then $Y \sim F$.