ANOVA : mean or variance? I am confused about the ANOVA method in Statistics.
ANOVA stands for analysis of variance.
It is used to compare the mean between several groups.
We use a test of variance (Fisher) for ANOVA.
So, is it a test of mean or variance?
 A: It's a test of means and, like the t-test, it uses the variances to do the test.  
How does that work?
If you have some groups with scores on some variable, then there will be variation within each group (because not all members are exactly the same) and between groups (because groups differ).  If the variation between is much larger than the variation within, then there is a lot of evidence that the means are different.  If the variation within groups is larger, then there is little evidence that the means are different.
For example, consider this case:
Group 1:  10, 10, 11, 11, 10, 9, 10, 10, 11, 9
Group 2:  12, 13, 14, 12, 13, 14, 12, 12, 12, 13
Group 3: 8, 8, 9, 9, 7, 7, 8, 8, 9
Intuitively, these groups seem different.  Compare that to:
Group 1:  10, 15, 6, 15, 6, 14, 5, 15, 6, 9
Group 2:  12, 20, 7, 16, 10, 10, 16, 12, 18, 7
Group 3:  0, 16, 15, 4, 12, 2, 4, 12, 9
The means of the three groups are the same in the two cases.  But in the second, it seems less clear that the means are really different. It could just be noise.  
