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    Re: Lunar distance accuracy
    From: Alexandre Eremenko
    Date: 2007 Oct 25, 12:23 -0400

    
    Dear Frank,
    
    > Alex often gets annoyed when I say that beginners can get
    
    The main disagreement we have on this matter
    is not about "novices". After all, my own very first Lunar
    in my life (made shortly after I purchased my first sextant)
    and posted on the list, was a PERFECT result.
    There is no doubt that "beginners CAN".
    In the sense that "some beginners sometimes can".
    
    The main point as I understand it is that we evaluate
    the same data very differently. We use different numbers
    derived from the same series as indicators access "accuracy".
    If the "average error" of some long series of observations
    (taken over the preiod of weeks or months, like in
    the case of White) is say 0'2, then what does this tell you
    about accuracy?
    Very little, indeed.
    In a real-life situation you don't want to risk a chance
    of hitting some rocks with 5% probability, do you?
    
    By the way, the measures like "quadratic mean" or
    "the most probable error" are also poor measures of accuracy.
    My recent analysis of White, Bolte and my own observations
    shows that
    a) distribution of errors is FAR from normal. Which means
    that the usual measures of dispersion cannot be applied.
    b) they are especially far from normal in their "tails".
    That is there are MORE LARGE ERRORS
    than a normal distribution
    would suggest.
    
    Indeed, in the 42 observations of White, we have
    one error of 0'.8 and 3 errors of about 0'.5
    in the distance.
    
    And I say that all available data contain a certain
    substantial proportion of such outlayers.
    You can call them blunders if you wish.
    
    My 121 observations in spring 2007 are as good as White's.
    They contain 13 individual shots with the error 0'.5,
    2 shots with the error 0'.6 and one with the error 0'.8.
    
    The error of the average is 0'.0.
    The average error is 0'.2. If I believe
    that this
    0'.2 is a "reliable indicator of accuracy" and then
    even multiply it by 2 "for safety", I will
    "hit the rocks" 18 times out of 120 !
    
    My experience and all available data show that the errors
    cwin the range 0.5 and more are UNAVOIDABLE,
    and occur perhaps in 10%
    of all observations.
    This is the main point of our disagreement.
    
    Alex.
    
    P.S. Bolte, White and my own observations of last spring
    are now posted on my web site under
    http://www.math.purdue.edu/~eremenko/accuracy.html
    I will soon add a digest of Bolte in English,
    as well, as my own statistical analysis of
    all these observations.
    
    
    
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