"Scheltema, Karen" wrote:
>
> I am spacing out on a formula, and my textbooks haven't been too helpful.
> Suppose I have 2 groups. What I want to do is come up with a weighted
> variance estimate for the combination of the two groups given s1, s2, w1,
> and w2.
By "weighted" do you mean "weighted based on the sizes of the two
groups"? If not, there are many possibly correct ways to weight; you
will need at least a criterion to select one.
You will also need the means of the two groups, or to know
that they are the same! That is:
aa aa a a bb bbb b
has much more variance than
aa aa abbabbb b
does, though the groups are identically distributed. However, this is a
very artificial-looking problem; if the two groups have plausibly
different means you should first ask whether the variance is a useful
description of a bimodal distribution!
If you are assuming the means to be the same, the situation is
more natural. Then you basically undo the square-root and
divide-by-(n-1) parts of the variance calculation, pool the
sums-of-squares, and divide by (n-2) [because you have *two* tagalong
sample means as your centers]:
s^2 = (n1-1) s1^2 + (n2-1) s2^2
---------------------
n1 + n2 - 2
If you had the original data you could pool them and get a slightly
better estimate; I'm assuming that you are doing this because you don't.
-Robert Dawson
.
.
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