[d2n-analysis-talk] Statistical Error Discussion

[Lamiaa El Fassi]

 Hi Dave,

 Those are my comments about the first two pages; labeled with error(1) and
error (2),
 of your PID efficiency document:

1. In fact, I didn't get your efficiency definition in page 3
  In my understanding, if eff= N_f / N_i. That means:
  N_f is the number of events selected in one particular detector f
  N_i is the number of events in any other detector excluding the detector f

For example, the PR efficiency is the ratio of events after adding the PR
cuts and the
total events with only Cerenkov cuts. Did I missing something?

2. For the standard error calculation of your efficiency (eff= N_f / N_i)
factor in page 4,
   you may consider it as the square of the derivative of the product of two
terms N_f and 1/N_i.
   So you need to have a (+) sign instead of (-) in your equation (2)

  Eq 2: (delta_eff)**2 = (1/N_i)**2 * (delta_N_f)**2 + (N_f)**2 *
delta_(1/N_i)**2
           With:
                    delta_(1/N_i) =  - delta_N_i / N_i**2

            So,

                  (delta_eff)**2 = (1/N_i)**2 * (delta_N_f)**2 + (N_f)**2 *
(-1/N_i**2)**2

                                      =  (delta_N_f / N_i )**2  + N_f**2 *
(delta_N_i / N_i**2)**2


    Eq 3: (delta_eff/eff)**2 = (delta_N_f / N_f)**2 + (delta_N_i/N_i)**2

    Eq 4:  delta_eff = eff * square root ((delta_N_f / N_f)**2 +
(delta_N_i/N_i)**2)


 In case you are interested I have a good book about the analysis error
calculation in my office.
 But unfortunately I forgot its name for the moment, I can give it to you
tomorrow.

 Cheers,

 Lamiaa


On Sun, Dec 13, 2009 at 5:57 PM, David Flay <flay at jlab.org> wrote:

> Hi all,
>
> I wrote up a short discussion on my methodology behind calculating error
> bars on the efficiencies:
>
> http://www.jlab.org/~flay/stat_error_12_14_09.pdf<http://www.jlab.org/%7Eflay/stat_error_12_14_09.pdf>
>
> Tell me what you think -- feedback is appreciated!  Maybe we can talk
> about these kinds of things
> at the informal discussions over lunch this week?
>
> See you all this week at the meeting(s)
>
> Dave
>
> -------------------------------------------------
> David Flay
> Physics Department
> Temple University
> Philadelphia, PA 19122
>
> office: Barton Hall, BA319
> phone: (215) 204-1331
>
> e-mail: flay at jlab.org
>              david.flay at temple.edu
>
> website: http://www.jlab.org/~flay <http://www.jlab.org/%7Eflay>
> -------------------------------------------------
>
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