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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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