# Propagating errors

Michael Lonetto lonetto at cgl.ucsf.edu
Sun Jul 7 14:01:40 EST 1996

```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
=-=-=-=-=-=-=-

```