Re: Rolling up variance


Jack Tomsky wrote:

Jack Tomsky wrote:
I hade a nice formula that "rolled up variance"
on a
set of
observations. For example, If I had a set of 100
observations, but
knew only the variance of x1 throu x50 and the
variance of x51 through
x100, I could calculate the variance of the
entire
population of
x1-x100. In other words:

Var(x1-x50) = 197
Var(x51-x100) = 233

then with "super formula" I could calc that
var(x1-x100) = 213

without having the 100 observations available to
me.

Anyone have an idea?

Thanks!
DB01



You would need the subgroup means as well.

Jack, while I am not disputing what you said to be
applicable
under certain assumptions, my FIRST question to both
you and
the OP would be to STATE your assumptions, because I
know
with 100% confidence that your formula and
conclusions would
wrong (or at least worthless) if the

variance from x1 through x50 and from x51 through
x100

were from samples from a Cauchy distribution. :-)

-- Reef Fish Bob.



Use the identity that in your case of two equal
size subgroups,

Sum(Xi-Xbarbar)^2 = Sum(Xi1-Xbar1)^2 +
Sum(Xi2-Xbar2)^2 + 2*(Xbar1-Xbar2)^2.

Here, Xbarbar is the mean of the 100, Xbar1 is the
mean of the first 50, Xbar2 is the mean of the last
50, Xi1 are the first 50, and Xi2 are the last 50.

Jack


Bob, I am assuming that the OP is talking about the sample variances. He is given the sample variances for each of the two subgroups. To get the sample variance for the entire sample of 100, he also needs to know the sample subgroup means. The formula I gave is an algebraic identity which can be used to obtain the sample variance for the complete sample. I assumed that when he said "entire population", he really meant "entire sample".

Jack

I should have made the smiley more prominent in

RF> > were from samples from a Cauchy distribution. :-)

Yes, I know both you and the OP were talking about the sample variance.
I think you missed my point that the sample variances you talked about
could have come from DATA from a Cauchy distribution, in which case
it doesn't make sense to even talk about a sample variance when
the population from which the sample came has an infinite mean
and an infinite variance.

So, no matter how you combine the two sample variances, none of the
sample variances make any statistical sense.

Or to put it another way, what CAN one DO with the sample variance
of a SAMPLE that is known to have come from a Cauchy population?

-- Reef Fish Bob.

.

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