Re: Roberts versus Lazio on "Overaveraging"
From: Tom Roberts (tjroberts_at_lucent.com)
Date: 01/19/05
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Date: Wed, 19 Jan 2005 06:41:53 GMT
greywolf42 wrote:
>>Joseph Lazio <jlazio@adams.patriot.net> wrote in message
>>news:llis6aghwh.fsf@adams.patriot.net...
>>>This is Data Analysis 101. Let your detector be anything you want it
>>>to be. Let it measure temperature on the sky, volts out of a
>>>voltmeter, whatever. If you take a long data stream from it, you can
>>>easily measure well below the "resolution" of the detector.
>>> [later]
>>>it is well known that one can make specific kinds of measurements
>>>below the resolution limit of an instrument,
>
> Joseph, *why* do you keep repeating this silly statement? Many people make
> such claims, but it is not valid science or statistics. You can easily show
> me wrong, by directing me to a statistics treatise on how to perform
> measurements below the resolution of the instrument used.
N.C.Barford, _Experimental_Measurements:_Precision,_Error,_and_Truth_.
This is old and elementary, but it's what we used in the version of
"Data Analysis 101" I took 30-some years ago.
I do not disagree with what Joseph Lazio wrote above. But greywolf42's
lack of knowledge and inability to read have apparently caused him to
think otherwise. This is all well known, and is indeed "Data Analysis
101" -- greywolf42 explicitly displays his ignorance here.
> Tom Roberts (and Bill Rowe), on the other hand, have many times called such
> processes "overaveraging" (at least when it is applied to experiments that
> would otherwise disprove SR). i.e.:
> http://www.google.com/groups?selm=vrd5jhksdt685b%40corp.supernews.com
>
> "And results reported implying an order of magnitude improvement in
> resolution over the best the instrument can achieve are very dubious."
Yes. A discussion:
For a basic measurement like that of the width of my desk, a given
technique has a given resolution. For example this meter stick is marked
in millimeters, and I can read it to about 0.2 mm resolution. So using
it to make a single measurement of the desk, I obtain an answer accurate
to ~0.2 mm. If I make a series of such measurements that are
STATISTICALLY INDEPENDENT I can improve that accuracy to the limit of
the systematic errors involved, by averaging multiple measurements. To
make them statistically independent, in this case I must re-apply the
meter stick to the desk for each measurement (merely re-reading the
scale without repositioning the stick would not give independent
measurements). As is well known, under these conditions, the mean of the
multiple measurements approaches the actual value to within an error
determined by the systematic errors combined with the intrinsic error of
the meter stick (~0.2 mm) divided by the square root of the number of
measurements contributing to the mean. In this case, some of the
systematic errors are:
errors in scribing the marks on the meter stick
optical parallax
temperature difference in the meter stick between its
calibration and use
It should be clear that none of these error sources are affected by
averaging, and they are related to the meter stick's construction and
manner of use. Now the manufacturer of the meter stick knows about these
systematic errors, and does not make heroic efforts to reduce them below
a human's ability to read and use it, so they are not enormously smaller
than ~0.2 mm. That applies to essentially any instrument. That's why
averaging many readings is highly suspect when someone claims an
improvement of an order of magnitude over the intrinsic resolution of
the instrument.
[For instance, wear on the end of the stick can be comparable
to that accuracy. That's why the 0 mark is not at the end.]
In the measurments greywolf42 references above, on which I commented
that they involved overaveraging, the experimenters claimed an
improvement of more than an order of magnitude by averaging. None of
them could claim their systematic errors were samll enough to justify
that smaller resolution. Moreover, most of them had a clear human bias
in roundoff, which makes multiple measurements be statistically
correlated, which means that averaging does not improve the actual
resolution of the mean below the amount of roundoff.
For instance, if when reading that meter stick I always
rounded up to the next millimeter, it should be clear that
the value I obtain will be larger than the actual value,
and no amount of averaging multiple measurements will
improve the accuracy of the measurement below ~0.5 mm.
Tom Roberts tjroberts@lucent.com
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