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[Phys-L] Re: Average earlier or average later?



Ludwik!

pse post the source code.

bc, who thanks Ludwik for his first copy of TB.

ludwik kowalski wrote:

On Sep 9, 2005, at 11:42 AM, Pamela L. Gay wrote:


Okay I'm game for a simulation. Played with excel for 30 seconds and
for
N = 1000
<X_N> = 2.200
stdev(X_N) = 0.374

I found
Y= Sum over N (X_N)^4 / N = 27.499
Y = <X_N>^4 = 23.423

On Sep 9, 2005, at 11:23 AM, ludwik kowalski wrote:


cut


I do not know how wide was the distribution of T in Pamela's
simulation. It turns out, as intuitively expected, that the discrepancy
between the true Y and the predicted Y grows rapidly when the
distribution of T becomes wider. This is shown below. I am talking
about averaging at the level of Y; averaging at the level of T produces
a nearly perfect prediction at any standard deviation. Like Pamela, I
used 1000 simulated measurements for each sigma and the mean T=2.2. My
distributions of T were Gaussian.

stdev predicted Y comment
0.0001 23.426 nearly perfect because all T are
practically identical
0.1 23.71 not a large systematic error when the
distribution of T is narrow (+/- 4.5%)
0.25 25.32 stdev is 22.7% of the mean T. It
produces a larger systematic error
0.50 30.25 even larger systematic error due to the
wrong way of averaging.
0.75 42.39 Very big systematic error (factor of 1.8)
1.00 60.40 Factor ~2.6

Ludwik (happy to find an old True Basic on the cloned drive)

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