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Topic: How to combine the standard deviations of multiple data subsets
Replies: 6   Last Post: Nov 23, 2012 1:26 PM

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Jim Clark

Posts: 79
Registered: 12/6/04
Re: How to combine the standard deviations of multiple data subsets
Posted: Oct 7, 1999 6:52 AM
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On Tue, 5 Oct 1999, Henry wrote:
> On Mon, 04 Oct 1999 21:35:27 GMT, (Henry) wrote:
> >On Mon, 4 Oct 1999 14:29:17 -0600, "Steve Schnick"
> ><> wrote:

> >>If one has several subsets of a given data set, and the mean, count,
> >>and standard deviations for each of these subsets, how can one
> >>calculate the combined standard deviation of the data subsets? i.e.,
> >>if the subsets were lumped together into one set, how does one
> >>calculate this new standard deviation?

> He did and my reply was:
> "Suppose data is Mi (the means) Ci (the counts) and Vi (the variances)
> The overall count is C = sumof(Ci)
> The overall mean is clearly M = sumof(Mi.Ci) / C
> The overall variance is V = sumof(Ci.(Mi-M)^2) / C + sumof(Ci.Vi) / C
> or equivalently V = sumof(Ci.[Vi+Mi^2]) / C - M^2
> No guarantee on this, but I think it is right."

I have no reason to think the above is incorrect, but I would
have conceptualized this problem using ANOVA approach.

V = SStotal/(N-1) = (SSwithin+SSbetween)/(N-1)

SSwithin = sumof(Ni.Vi)
SSbetween = sumof(Ni.(Mi-M)^2)

Best wishes

James M. Clark (204) 786-9757
Department of Psychology (204) 774-4134 Fax
University of Winnipeg 4L05D
Winnipeg, Manitoba R3B 2E9

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