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    Re: Rejecting outliers: was: Kurtosis.
    From: Peter Fogg
    Date: 2011 Jan 1, 06:35 +1100
     George Huxtable writes:

    I was trying to discover exactly what Peter Fogg himself was actually
    claiming his procedure could accomplish.

    This is breathtakingly disingenuous, George, after the many, many posts which have collectively and comprehensively set out, and then repeated over and over, in as simple and clear terms as possible "what Peter Fogg himself was actually claiming his procedure could accomplish".  This has to go beyond disingenuous towards another territory. Let's call it silly, to be kind.
    Not what Frank Reed thought that
    it might accomplish, though those views may also be of some interest.

    Nature of this forum, George, anyone can chime in.

    And I used the word "magic" to describe that procedure, because nowhere,
    that I can recall, has Peter Fogg explained, in numerical terms that we
    might agree on (or otherwise) what his criteria are for accepting some
    observations and rejecting others.

    Now you are implying that you have failed to understand how this simple procedure works, George, which is getting silly again.  Why don't you try using it?  I have a feeling that this could be helpful in understanding it, if you are really struggling still.
    Which brought this response, from Frank-
    "Now come on, George. Magic?? I really believe that this attitude has made
    it nearly impossible for you to see something simple and useful."

    Oh? What is this "something simple and useful" that Frank believes my
    attitude has made it nearly impossible for me to see? Is it, I wonder, the
    virtue of plotting observations, to allow the practised eye to pick out
    oddnesses? Well, I'm all in favour of that, and can not recall any
    arguments I've made against it.

    As a one-time experimental physicist, such
    procedures have played a large part in my working life. And I see no reason
    why that should not apply to navigational procedures also. The human eye
    and brain can work together powerfully, and often provide a workable
    alternative to full mathematical analysis.

    Hallelujah!  George Huxtable has seen the light!  George has accepted the magic!  Oh happy day...  Its taken a while but you've made it to the heaven of reducing random error, George.

    Something I have been trying to explain recently is how problematical it must be to apply a "full mathematical [substitute 'statistical' perhaps] analysis" when the population of data sets is so restricted.
    What I have argued against are
    spurious claims that ascribe some exceptional qualities to those procedures
    that they do not, and cannot, possess.

    Very sound.  If only there were any "spurious claims" for you to have argued against... 

    Now let's get on to the real nub of this discussion, the separation of
    "outliers" from what I will call useful data.

    I am aware that a Gaussian distribution is no more than a convenient
    approximation, representing observed scatter in measurements of many types,
    that seems to work well in practice. And there are many reasons why some
    observations might well lie outside an expected Gaussian error-band: they
    are commonly ascribed to some sort of "blunder". Such blunders can come in
    all sorts of unpredictable shapes and sizes, and it would seem impossible
    to predict any frequency-distribution for errors of that type. They would
    certainly corrupt any set of otherwise-valid measurements, and need to be
    detected and discarded, to the extent that is possible. That is the
    challenge that mariners face, to somehow distinguish the good from the bad.

    Yes, it is.  And this is the glaring defect of blindly averaging.  Doesn't give you any opportunity to "somehow distinguish the good from the bad".  The slope does.
     If there's an observation that you have a "funny
    feeling" about, or put a question mark against, the moment to discard it is
    there and then, at the time of the "funny feeling". Not wait to see if it
    fits in with your preconceptions or not, and then discard it if it doesn't.

    I beg to differ.  I propose that it could be useful to plot that sight along with the others observed over a short period of time and compare their pattern with the actual slope, the slope indicating the pattern they would follow except for random error.  Then it certainly could be useful to recall and take into consideration the "funny feeling" relating to that sight during analysis.

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