Hi, I am looking at ANOVA and seem to be missing something. As I understand, the point of ANOVA is to determine whether treatment means are the same or not. So why is the ANOVA test an F test that tests the variance of the treatment means? The treatment means could be different even if they have the same variance. Thanks.
I'm also unclear on this. If both the numerator and the denominator of the test statistic were huge numbers, but the denominator was much the bigger of the two, then the test statistic would be low presumably leading to us not rejecting H0. However if the numerator (the variability between means) is very large, surely the treatment means must be different even though we have not rejected H0?
