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> I was wondering if someone could enlighten me as to the relevance of the
> geometric mean when applied to the calculation mode for log amplified data.
> My understanding of the arithmetic mean is
> mean = (x1 + x2 + x3 ...+ xn) / n
>
> whereas the geometric mean is
> geo_mean = nth root of (x1 * x2 * x3 ...* xn)
>
> which yields a slightly different answer.
> Any info will be appreciated.
In my attempts to emulate, in my own programs, the means and medians
for log-acquired data given by the Becton-Dickinson FACSCAN and
FACSTAR software, I succeeded for the mean by calculating the log of
the arithmetic mean of the antilogs of the observations (channel
values representing logs of fluorescence intensity). Thus, for the
mean of log-acquired data, B-D gives the log of the mean value that
would have been obtained had the data been acquired with linear,
rather than log, amplification. The same principle applies to the
median in the case where there are an even number of observations (so
the median falls "halfway" between the middle two). I was pleased to
see such care applied in the development of their software.
I, too, thought that the geometric mean should give the same value but
it appears to give a different value. Hopefully someone else can clarify
this issue.
-- /* - - - - - - - - - - - - - - - - - From - - - - - - - - - - - - - - - - - - Eric Martz Associate Professor Morrill IVN Rm 203 Voice 413-545-2325 of Immunology Dept Microbiol, Univ Mass FAX 413-545-1578 Amherst MA 01003 USA emartz@titan.ucc.umass.edu - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
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