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In reply to my explanation, that it was unjustified to claim that
averaging 4 observations resulted in a halved error, except when those
observations were statistically independent, Frank Reed replied-

| It is no "assumption", George. It works in practice, again and
again. Or I
| should say, it works 'for me' again and again, and that's why I
recommend  it.
| Also, in the log books of vessels from the early 19th century, you
frequently
| find references to averaging four or more observations. This was
standard
| historical practice.

Averaging four such observations will certainly do no harm, and I did
not, and do not, criticise such a practice. It will reduce, to some
extent, the resultant error, depending on what part of the error was
random, and what part of the error repeats each time.

However, unless any systematic component is entirely lacking, Frank's
claim that the error will be halved remains invalid. And we have seen,
by examining the origins of such errors, that much of the overall
error is systematic, and will repeat, exactly the same, from one shot
to the next. That part of any overall error is not reduced by
averaging successive observations. Frank is not immune from the laws
of statistics.

George.

contact George Huxtable at george@huxtable.u-net.com
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.


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