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    Re: Cocked hats, again.
    From: George Huxtable
    Date: 2007 Mar 15, 22:35 -0000

    Oh, there's endless mileage in this cocked hat question, isn't there?
    
    Peter Fogg (alias PF) wrote-
    |
    | George Huxtable advocates this "simple message":
    | >  "Plot a point, at the centre
    | > of the triangle, but be aware that the true position could lie
    well
    | > outside that triangle."
    |
    | Since this is a somewhat "tendentious" (lovely word, that) argument
    | about statistics, isn't the chance of the "true position" lying
    within
    | one standard deviation of a position line about 70% ? (Whilst
    | retaining the assumption of a standard distribution of error.)
    
    Yes it is.
    
    | And within two standard deviations about 90% ?
    
    Yes it is.
    
    | Is it not correct that the most likely place to find this "true
    | position" is close to the position line?
    
    Yes it is.
    
    Those statements are all compatible.
    
    | What evidence can you present, George, for the "true position" being
    | at all likely to lie "well outside" the triangle - or other shape?
    
    The words I used were these-
    
    ""Plot a point, at the centre of the triangle, but be aware that the
    true position could lie well outside that triangle."
    
    I am unsure what Peter is objecting to here. Is it to the word "well"?
    
    I have presented a logical argument, which nobody so far has yet
    discredited, that three times out of four, the true position will lie
    SOMEWHERE outside the triangle. If Peter can disprove that, well and
    good; we will take him seriously. For what it's worth, I have checked
    it against a computer simulation, but I place little reliance on such
    things.
    
    That in itself gives little information about HOW FAR outside the
    triangle the true position might lie, in those three times out of
    four. But note that, from one trial to the next, the triangle varies
    in shape and size due to the random errors in each intercept.
    Sometimes, just by chance, the triangle will turn out to be a
    particularly small one. And if you make just one trial, there's no way
    of telling from the result that the triangle is unusually small. But
    when that happens to be the case, it's likely that the scatter,
    between the true position and the centre of the triangle, may put them
    apart, by an amount that's many times the "size" of that small
    triangle. So, if a single error-triangle is all you have to go on, you
    have to accept that its size tells you little about the possible
    amount of the scatter. It may suggest a lower-limit to the scatter,
    but not an upper-limit.
    
    If Peter disputes my statement that he questions, I ask him to explain
    his own view of the relation between the true position and an
    error-triangle.
    
    George.
    
    contact George Huxtable at george---.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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