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    Re: Position Lines and a Systematic Error
    From: Trevor Kenchington
    Date: 2003 May 30, 22:13 -0300

    Jared Sherman wrote:
    
    > A circle of error may still be needed to accomodate other factors, but at 
    least the inherent error RANGE in each sighting is immediately visible when a 
    simple wide stroke is drawn.
    
    
    I applaud Jared's intent. (I get to waste far too much energy arguing
    with scientific colleagues who present their point estimates and grossly
    misrepresent the massive uncertainties surrounding them. It makes me
    sensitive to questions of precision of measurements.)
    
    One caution though: Drawing two "fat" LOPs will result in a
    parallelogram of overlap which would then seem to represent the area
    within which the true position most probably lies. That would, however,
    be unduly pessimistic.
    
    If the errors in the LOPs are largely random (rather than systematic),
    then it is most unlikely that both of a pair of LOPs will have high
    errors. If there is a 95% chance that each LOP passes within 4 miles of
    the true position, then there is a 5% chance that one LOP is 4 miles or
    more from that position. But there is only a 5%x5% = 0.25% that both
    LOPs are so far off the mark.
    
    In more practical terms, the contour surrounding the probable area in
    which the true position lies will be an ellipse drawn inside the
    parallelogram formed by the margins of Jared's two thick lines. The
    likelihood that the true position lies in one of the corners of the
    parallelogram is very low.
    
    
    Of course, in an ideal representation, Jared's lines would be drawn with
    soem computer graphics set up that could make the centre of each line
    near-black while it faded away to a very pale grey on either side. At
    least, I suspect that the random errors have a somewhat "bell-shaped"
    distribution, such that most LOPs are not so far from the true position
    even though a few are a long way off. Such complex plotting is not, of
    course, either needed or practical.
    
    
    Trevor Kenchington
    
    --
    Trevor J. Kenchington PhD                         Gadus{at}iStar.ca
    Gadus Associates,                                 Office(902) 889-9250
    R.R.#1, Musquodoboit Harbour,                     Fax   (902) 889-9251
    Nova Scotia  B0J 2L0, CANADA                      Home  (902) 889-3555
    
                         Science Serving the Fisheries
                          http://home.istar.ca/~gadus
    
    
    

       
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