Is there an extension to the F-test? I'm new to statistics but I come from a mathematical background. So while learning about the t-test, which compares sample means, and the f-test which compares variances is was wondering if there is an extension to the f-test (correct me if I'm wrong), similar to the ANOVA for the t-test?
ANOVA is "used to analyze the differences among means (from Wikipedia)". So, as far as I understand it, it is an extension to the t-test.
I did some research and found out about the Bartlett's test, which in my understanding would be an extension to the f-test, is that correct?
My confusion comes mainly from how the terms are used in some software. For instance g*power. Here the anova is found in the section of the f-tests, which doesnt make any sense to me...

The F test for ANOVA uses the ratio of two quantities, which when the population means are equal (and the assumptions hold) will both be independent estimates of $\sigma^2$. The one on the numerator estimates it from variation in group means, the one on the denominator estimates it from within-group variation about the group means (which will be consistent for $\sigma^2$ even when the population means differ).
When $H_0$ is false the numerator is biased upward as an estimate of $\sigma^2$, since it's got the effect of the variation in population group-means (under the alternative, the statistic is distributed as noncentral F).
That is, it is still effectively using a test for equality of two variance estimates, but it's using that to test equality of population means.
