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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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