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    Re: Rejecting outliers
    From: Fred Hebard
    Date: 2011 Jan 1, 15:33 -0500

    Peter,
    
    Those are simulated data, not real data.
    
    Fred
    
    On Jan 1, 2011, at 2:37 PM, P H wrote:
    
    > From: Fred Hebard
    >
    > All of this discussion could be informed immensely by some data and
    > associated analyses.  Data talk.
    >
    > ======================================================================
    > =======
    >
    > In the attached files I modified my earlier example as follows:
    >
    > file source_data.png:
    > The six altitudes (column C, with #5 off from the linear trend by
    > only 1 degree this time) are changed by a random number between
    > -0.5 and 0.5 (column B).  Column D (=C+B) is entered as input into
    > column B in average1.xls.
    >
    > file average1.xls:
    > "Resolution" in F16 was changed to 0.5 degrees to roughly coincide
    > with the spread of the random scatter in the data.
    >
    > The averaged value at UT=12:40:00 (when the "bad" altitude of
    > 14.978 happened) is calculated to be 14.171, which is better than
    > H0=14.318 (file altitudes.png, cells J24, J25 in average1.xls)
    > produced by the initial non-weighted least squares fit.  In file
    > weights.png we can see that the "bad" data point is not completely
    > removed from consideration but its influence on the final fit is
    > reduced by the factor of 1.536 / 4 relative to the other five
    > "good" data points.  The number "4" you see in column BL is 1 /
    > "Resolution"-squared.
    >
    > The difference | H0-H_fit | = 14.318 - 14.171 = 0.147 could serve
    > as a ballpark indicator of how much uncertainty is associated with
    > this result.
    >
    > Thus, an outlier is identified and not allowed to completely skew
    > the final result (Peter Fogg's concern). However, unless it is
    > really crazy like my earlier 66, it is not completely removed from
    > the data set, either (Geoffrey Kolbe's concern).  The calculated
    > weights express how important each data point is considered by this
    > procedure to be (George Huxtable's concern).  I propose the | H0-
    > H_fit | quantity as a guide to what extent the final result can be
    > trusted, which is every navigator's concern.  Sure, this does
    > require a computer which may not work when needed, that is always a
    > possibility; but that is true for all machines to some extent,
    > including chronometers and sextants.
    >
    > Happy New Year to all!   :-)
    >
    >
    > Peter Hakel
    >
    >  ls>
    
    
    
    
    

       
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