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    Re: Latitude by Lunar Distance
    From: George Huxtable
    Date: 2006 Nov 13, 15:52 -0000

    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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