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Re: systematic error and statistical error



This time I can confess I haven't been paying close attention to this
thread, but it may well be we have some different definitions of systematic
error.

Many years ago when I was doing nuclear mass measurements, we always kept
track of uncertainties that we knew would be only in one direction but
couldn't determine the actual magnitude other than for an upper limit. For
example, our data were particle tracks in photographic emulsions that had to
be counted under a microscope as a function of position (where the emulsions
had been in a magnetic spectrograph). There were always uncertainties in
the counting, but these would always be low counts rather than high counts.
Since the peak shapes were split guassian, errors in the counting would push
the 1/3 height of the peaks (used with a calibration to determine energies)
toward lower values. So any error in counting would always lead to lower
values but we could only put an upper limit on the expected counting error.
We had several such uncertainties some tending to higher values, some
towards lower. We also had the normal kind of random uncertainties. In the
end, we combined the systematic errors algebraically and the random errors
in quadrature. As I remember, we then combined the overall statistical
error with the overall random error in quadrature--but that was 25 years ago
and I don't have my thesis handy. ;-(

Rick

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Richard W. Tarara
Associate Professor of Physics
Saint Mary's College
Notre Dame, IN 46556
rtarara@saintmarys.edu

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----- Original Message -----
From: "Miguel A. Santos" <msantos@ETSE.URV.ES>
To: <PHYS-L@lists.nau.edu>
Sent: Tuesday, October 10, 2000 12:16 PM
Subject: Re: systematic error and statistical error


Hi Ludwik,
it seems to me that what you call here 'systematic error'
is actually a bias. Aren't you mixing both concepts?

On the other hand, one can never get rid of systematic
sources of errors: The finite precission of any apparatus
introduces such a systematic error. And this is unavoidable.
Information on this source of systematic error is usually given
by the manufacturer, who has done a calibration of the apparatus.
In the absence of this information, the minimal interval you can
measure with your apparatus seems to me a reasonable estimate
(lower bound, if you want) for this systematic error.

Regards,
Miguel A. Santos
msantos@etse.urv.es