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?
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2It is a test for comparing means between different groups, but the tools of detecting a difference in means is based on assessing variance in and between groups. – Greenparker Apr 20 '16 at 18:07
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why don't we compare the mean between each group then, as for the t test? – rom Apr 20 '16 at 18:29
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2It is the variance of the group means that is being tested when one tests for mean differences. Note that the group means differ if and only if there is >0 variance in the group means. So testing the variance of the group means is the same as testing for group mean differences. – Jake Westfall Apr 20 '16 at 19:26
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3Possible duplicate of Good resource to understand ANOVA and ANCOVA? – kjetil b halvorsen May 28 '17 at 18:30
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@kjetilbhalvorsen It's sort of a duplicate of that, but that question specifies that the user has a "good math background" which may not be the case here. – Peter Flom May 30 '17 at 11:28
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@Peter Flom: So what to do in such cases? – kjetil b halvorsen May 30 '17 at 11:54
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A lot of students are confused by this. There is a detailed explanation here. – David Lane May 30 '17 at 14:38
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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.
Peter Flom
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