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    Re: Rejecting outliers: was: Kurtosis.
    From: Geoffrey Kolbe
    Date: 2010 Dec 31, 22:21 +0000

    George wrote:
    >The threadname is changed once again, from "kurtosis" (a mathematician's
    >word far beyond the vocabulary of navigators, which displays Frank's
    >erudition) to the more familiar "Rejecting outliers", which is what the
    >discussion seems to be really about.
    >I was trying to discover exactly what Peter Fogg himself was actually
    >claiming his procedure could accomplish.
    >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.
    I have to say that I share George's disquiet about the notion of
    rejecting outliers simply because they do not seem to fit with the other data.
    Perhaps it is that, like George, I have a background as an
    experimental physicist, and that the notion of rejecting some data
    simply because it does not sit neatly with the rest of the data is an
    anathema. Experimental data is usually messy and experience shows
    that a lot can be learned from consideration of the possible causes
    of outliers. Simply ignoring outliers as "bad data", without which
    the data set would look a lot prettier and be a lot more impressive
    in the publication, can come back to haunt one in the end when
    someone (usually oneself) repeats the experiment....
    Frank said that the rejection of outliers was quite acceptable and
    directed me to look (for example) at Chauvenet. I promised I would
    and I did. (Volume two, page 558, "Criterion for the rejection of
    doubtful observations") It seems to be a Chi Squared test based on
    two or more purely random, Gaussian, distributions. Chi Squared tests
    are useful if the data cannot be repeated - such as for observations
    of a rare astronomical phenomena or a space borne experiment - and
    you are trying to wring the last bit of precision from the data. But
    applying such a statistical sledge hammer to a set of five or six
    sextant altitude sightings is - I respectfully submit - hardly
    worthwhile. The navigator's time would be better spent taking another
    round of sights to force better precision on the mean than applying a
    statistical eraser to doubtful data.
    Even if taking more sights is not practical, outliers should not be
    discarded unless a good reason presents itself as to why they should
    be discarded.  The consequence may be a rather more open cocked hat
    or a fix of somewhat looser precision than one would like. But better
    that than discarding "bad data" and risk a false sense of security
    from the resulting tight fix.
    Geoffrey Kolbe

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