# Propagating errors

Gerard Tromp tromp at sanger.med.wayne.edu
Mon Jul 8 12:28:36 EST 1996

```Helo Michael,

The standard error of a quotient (sigma-quotient) of two means (x-bar1 and x-bar2)
which are mutually independent is:

[sigma-quotient/quotient]^2 = (sigma1/x-bar1)^2 + (sigma2/x-bar2)^2

sigma-quotient^2 = quotient^2 * [(sigma1/x-bar1)^2 + (sigma2/x-bar2)^2]

sigma-quotient  = {quotient^2 * [(sigma1/x-bar1)^2 + (sigma2/x-bar2)^2]}^1/2

Hope it helps.

Michael Lonetto wrote:
>
> Hi,
>
> I have a question about calculations on datasets, each with separate
> errors.  For example :-)
>
> I have three data sets, each of which has a mean and a standard
> deviation.
>
> Set 1 is a control (eg, no trascription activator)
>
> Sets 2 and 3 are results with mutant and wild type activators,
> respectively.
>
> Dividing the means of sets 2 and 3 each by set 1 provides a measure
> of transcription activation.
>
> The question is, what to do about the errors:
>
> 1) since I'm using the same set as control for both sets 2 and 3 can
> I ignore the error on set 1?
>
> 2) If not, how can I combine the standard deviations?  Simple combinations
> (divide, multiply) do not produce reasonable numbers :-)  Adding them
> isn't too bad, but not of obvious validity.  Should I average the
> coefficients of variability and normalize them to the activation ratio?
>
> Any way that I do this I see differences well beyond the spread of the
> data, the question is what is the proper thing to do?
>
> Sorry for posting this to bionet.software, but I remember seeing a
> similar query some time back (and wondering at the time why anyone
> would care :-0)  I can't find any discussion of this problem in
> BIOMETRY or my other statistics book.  Any pointers to an appropriate
> source will be appreciated.
>
> Thanks, Mike
>
> --
> -=-=-=-=-=-=-            Mike Lonetto                   lonetto at cgl.ucsf.edu
> UCSF Dept of Stomatology, 513 Parnassus Avenue, San Francisco, CA 94143-0512
>                                                               =-=-=-=-=-=-=-

Gerard
--
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Gerard Tromp, Ph.D.
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