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    Re: Rejecting outliers: was: Kurtosis.
    From: Fred Hebard
    Date: 2011 Jan 1, 12:33 -0500

    All of this discussion could be informed immensely by some data and
    associated analyses.  Data talk.
    On Dec 31, 2010, at 6:50 PM, Peter Fogg wrote:
    > Geoffrey Kolbe wrote:
    > 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.
    > This puzzles me, Geoffrey, given the boundaries of the particular
    > context we are discussing.  You do understand that the calculated
    > slope can be assumed to be a fact? (ie; apart from being an
    > approximation of an arc, and assuming the DR is reasonable).
    > Therefore if you end up with a pattern of sights that more or less
    > follows that slope, but one (or more) apparent outlier that
    > obviously does not, what possible conclusion can be reached?
    > Either the pattern is generally correct and the outlier an obvious
    > indication of error, or the outlier is correct and the apparent
    > pattern then must be entirely composed of erroneous data sets.  It
    > seems to me to be a common-sense choice between these alternatives.
    > There is a third way, that of averaging.  This accords weight to
    > the apparent outlier(s) in proportion to population extent.  If
    > there are 2 outliers, both on the same side of the line, and a
    > restricted population (which is pretty-much a given) then
    > significant error can result.  Error that is easily avoided by use
    > of the slope.
    > Experimental data is usually messy and experience shows that a lot
    > can be learned from consideration of the possible causes of outliers.
    > I agree.  Use of slope allows for and encourages this
    > consideration.  Averaging does not.
    > 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.
    > You can't be serious.  Firstly; remember that one of the most
    > significant drawbacks to the use of celestial navigation in
    > practice is the weather.  Another is the limited extent of dawns
    > and dusks available (only 2 per day!) which offer the great
    > advantage of a multiple-body fix at much the same time, without
    > introducing error through running forward or back a position.
    > I suggest that the navigator's time would be better spent in
    > analysing the sights he/she has, and applying this simple technique
    > in order to reduce random error.
    > 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.
    > Once the slope has been calculated and the pattern of sights
    > compared with it, it is up to the individual navigator to make the
    > decision about the best place to place the slope amongst the
    > sights.  As much or as little weight can be accorded to any
    > apparent outliers as you like.
    > Frank seems to think that some pre-determined numerical quantity
    > can be applied to assist that decision.  Goodo.  Feel free to do
    > this if anyone wants to.  I doubt very much whether much of this
    > will ever happen in practice; one of the big advantages of slope is
    > its simplicity and relative ease of use.
    > The other very obvious point is that without slope how would you be
    > even aware of apparent outliers?  Not though blind averaging,
    > that's for sure.  If you only take one sight and then reduce that
    > then you have no idea of how good or bad that individual sight
    > might be.  Could be excellent.  Could be an outlier.  Could be
    > anything at all.
    > 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.
    > Half right.  The right part is that one should never assume that
    > any fix is entirely free of error.  However, remember that use of
    > slope is only one-half of a two-pronged approach; the half of
    > dealing with random error as best as can be practically done (until
    > someone comes up with a better method, which is somewhat different
    > to going to outlandish lengths to try to poke holes in this one -
    > eg; assuming a vastly wrong DR).
    > The other half of the two-pronged approach is to assume the
    > resulting position lines to be free of random error, leaving non-
    > random or systematic error to be dealt with.  This can be simply
    > and effectively done by bisecting the angles of intersecting
    > position lines, leading to a fix position where these bisecting
    > lines meet at a point.  It ain't perfect, but it can be reasonably
    > expected to be a better fix, with reduced extents of both random
    > and non-random error.
    > Nothing magic after all, George, Geoffrey et al.  Sorry.  Its
    > really only common sense powered via some simple drafting.
    > I've just given up resisting the temptation to add this (you can
    > think of this personal weakness as a kind of reverse New Year's
    > resolution):
    > Pourquoi faire simple lorsque, avec tellement peu plus d'effort,
    > l'on peut faire compliquer...

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