Just to answer Genya's message.
I am no doubt using the word correlated incorrectly and Genya, who
probably knows english better than I do, is confused by the mistaken
use. So let me make a simple analogy.
Suppose I stand at one end of the south hall and throw coins at a
garbage can. I throw N coins. Afterwards I go look in the garbage
can and count the number which landed heads up NH and the number
which landed tails up NT. I can form an asymmetry (NH-NT)/(NH+NT).
I consider this measurement correlated. I can repeat it many times
throwing different numbers of coins, drunk, sober, eyes closed,
whatever. (NH+NT) will vary from trial to trial. (NH+NT)/N will
vary from trial to trial. But the distribution of NH/(NH+NT), or NT/
(NH+NT), or (NH-NT)/(NH+NT) will be binomial and follow binomial
statistics. I consider this a correlated measurement.
Now for an uncorrelated measurement. One day I throw Nhi coins but
now only count the number that are heads up NHi. The next day I
throw Nti but only count the number that are tails up NTi. I can
normalise each rate as NHi/Nhi and NTi/Nti and form an asymmetry (NHi/
Nhi - NTi/Nti) / (NHi/Nhi + NTi/Nti) but now the NHi and NTi are
uncorrelated and the statistics are Poisson when I repeat this many
times. The only way I justify forming the asymmetry and drawing
meaning from it is if the conditions of the experiment are the same
every time.
BLAST isn't as bad as this last case as we flip spin and helicity
quite frequently and detector performance doesn't change quickly with
time but the measurements are still uncorrelated and thus the
statistics are Poisson not binomial. Also the results have to be
normalised in order to calculate an asymmetry and there is an
uncertainty associated with the normalisation that perhaps can be
neglected but perhaps not. The big difference is that correlated
measurements can be combined simply. Uncorrelated measurements can
only be combined is the same simple manner only if all the
normalisation factors are the same.
Bottom line: for BLAST -- you can't combine things simply.
Cheers,
Douglas
26-415
M.I.T. Tel:
+1 (617) 258-7199
77 Massachusetts Avenue Fax: +1
(617) 258-5440
Cambridge, MA 02139, USA E-mail:
hasell@mit.edu
On May 23, 2005, at 9:13 AM, Genya wrote:
> Here are my 2 cents.
> I support completele Doug's conclusion that the best way to
> handle multiple sets of
> data is to calculate the asymmetry in easc set separately and then
> sum them up, with a proper
> weighting of course.
> But I still can't take this "correlated asymmetries" thing,
> even if we are talking aboit left-right asymmetries.
> This approach implies, for instance, that if in the given day there
> is a statistical fluctuation, and Left sector
> detected more events than usually, then Right sector on this day
> should detect less events than usually... which
> is obviously wrong.
> The only correlation between counts in the Left and Right
> sectors comes from the actual change in the target thickness,
> and this correlation is direct rather than inverse... and dont
> affect asymmetries anyway.
> Genya
>
>
>
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