Hi Dave,<br><br> Those are my comments about the first two pages; labeled with error(1) and error (2), <br> of your PID efficiency document: <br><br>1. In fact, I didn't get your efficiency definition in page 3<br> In my understanding, if eff= N_f / N_i. That means:<br>
N_f is the number of events selected in one particular detector f<br> N_i is the number of events in any other detector excluding the detector f<br><br>For example, the PR efficiency is the ratio of events after adding the PR cuts and the <br>
total events with only Cerenkov cuts. Did I missing something? <br>
<br>2. For the standard error calculation of your efficiency (eff= N_f / N_i) factor in page 4, <br> you may consider it as the square of the derivative of the product of two terms N_f and 1/N_i.<br> So you need to have a (+) sign instead of (-) in your equation (2)<br>
<br> Eq 2: (delta_eff)**2 = (1/N_i)**2 * (delta_N_f)**2 + (N_f)**2 * delta_(1/N_i)**2<br> With:<br> delta_(1/N_i) = - delta_N_i / N_i**2<br> <br> So,<br> <br>
(delta_eff)**2 = (1/N_i)**2 * (delta_N_f)**2 + (N_f)**2 * (-1/N_i**2)**2<br> <br> = (delta_N_f / N_i )**2 + N_f**2 * (delta_N_i / N_i**2)**2<br>
<br><br> Eq 3: (delta_eff/eff)**2 = (delta_N_f / N_f)**2 + (delta_N_i/N_i)**2<br><br> Eq 4: delta_eff = eff * square root ((delta_N_f / N_f)**2 + (delta_N_i/N_i)**2)<br><br><br> In case you are interested I have a good book about the analysis error calculation in my office.<br>
But unfortunately I forgot its name for the moment, I can give it to you tomorrow.<br><br> Cheers,<br><br> Lamiaa<br><br><br><div class="gmail_quote">On Sun, Dec 13, 2009 at 5:57 PM, David Flay <<a href="mailto:flay@jlab.org">flay@jlab.org</a>> wrote:<br>
<blockquote class="gmail_quote">Hi all,<br>
<br>
I wrote up a short discussion on my methodology behind calculating error<br>
bars on the efficiencies:<br>
<br>
<a href="http://www.jlab.org/%7Eflay/stat_error_12_14_09.pdf">http://www.jlab.org/~flay/stat_error_12_14_09.pdf</a><br>
<br>
Tell me what you think -- feedback is appreciated! Maybe we can talk<br>
about these kinds of things<br>
at the informal discussions over lunch this week?<br>
<br>
See you all this week at the meeting(s)<br>
<br>
Dave<br>
<br>
-------------------------------------------------<br>
David Flay<br>
Physics Department<br>
Temple University<br>
Philadelphia, PA 19122<br>
<br>
office: Barton Hall, BA319<br>
phone: (215) 204-1331<br>
<br>
e-mail: <a href="mailto:flay@jlab.org">flay@jlab.org</a><br>
<a href="mailto:david.flay@temple.edu">david.flay@temple.edu</a><br>
<br>
website: <a href="http://www.jlab.org/%7Eflay">http://www.jlab.org/~flay</a><br>
-------------------------------------------------<br>
<br>
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