If I'm understanding the question, it's a fairness issue. :-)
The denominator (MSWithin) is the pooled variances of samples. The numerator,
OTOH, is a variance of sample means. In essence, then, the numerator is looking
at a sampling distribution of means. Because the sampling distribution of the
mean has a variance of (sort of) s2/n, multiplying by n turns it into s2, which
gives you an F (ratio of variances).
Hugh
On Feb 22, 2012, at 8:57 AM, Marc Carter wrote:
> Hi, all --
>
> I fear this to be a really stupid question, but...
>
> In ANOVA, why are the squared deviations in the SS between groups scaled
> (multiplied) by _n_? I was once told it was to weight them, but that somehow
> doesn't seem right.
>
> Can someone help?
>
> TIA,
>
> marc
>
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