Re: [BLAST_ANAWARE] Asymmetry calculations again

From: Chris Crawford (chris2@lns.mit.edu)
Date: Mon May 23 2005 - 13:09:20 EDT


Douglas Hasell wrote:

> 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.

  this is not an asymmetry the same as blast. the difference is that
each coin has a chance of becoming either heads or tails, where as for
a physics asymmetry, each electron is predetermined sigma_+ or
sigma_- depending on the beam and target conditions, and we are just
waiting so see how many per time come. so i would argue that the
asymmetry statistical errors is calculated from the poisson errors in
each yield, not from binomial statistics.
  i agree with your formula for adding asymmetries: A/dA^2 = sum_i
A_i/dA_i^2, where 1/dA^2 = sum_i{1/dA_i^2}, as long as you have
enough statistics for each A_i such the errors are approximately gaussian.
--chris

>
> 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
>>
>>
>>



This archive was generated by hypermail 2.1.2 : Mon Feb 24 2014 - 14:07:32 EST