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Re: statistical fluctuations



The standard deviation is 9.2, which is the square root of (47 + 37).

The signal is the difference between two measured values (10 = 47 - 37). By Poisson statistics, the variance of each measured value equals the measured value (47 and 37, respectively). The standard deviation of each measured value is the square root of the variance, or the square root of the measured value (square root of 47 and square root of 37, respectively). The variance of the difference between the measured values is the sum of the variances of the measured values (47 + 37 = 84). Therefore, the standard deviation of the signal is the square root of the sum of the measured values (square root of 84 = 9.2).

Daniel Crowe
Oklahoma School of Science and Mathematics
Ardmore Regional Center
dcrowe@sotc.org


-----Original Message-----
From: Ludwik Kowalski [mailto:kowalskil@MAIL.MONTCLAIR.EDU]
Sent: Friday, September 05, 2003 1:53 PM
To: PHYS-L@lists.nau.edu
Subject: Re: statistical fluctuations


In a private message Bernard Cleyet asked:

p.s. why "stat. flucts."?=A0 I think subtracting
background is more appropriate.

In my illustration one chip recorded 47 tracks
(signal plus background) while another recorded
37 (background). I subtract and obtain signal
equal to 10. But I can not say that signal=3D10
because both 47 and 37 would fluctuate from
chip to chip. The probability that the true signal
is 10 is very very small in this example.

Now consider the Oriani's method. (His numbers
were actually much larger, I made them small to
focus on fluctuations. Suppose that using his
method (one chip) I observe 37 before the
experiment and 47 after the experiment. I conclude
that the signal is 10. Yes, I do not expect that the next
experiment will yield the same signal but the result
will always be positive or zero. Is it correct to say
that the standard deviation for the signal should
be sqrt(10), in this illustration? I am not certain.
Ludwik Kowalski