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Bill:
> Excellent point from a practical standpoint IMHO.  You may recall a long
> series pd posts on averaging years ago where the academic viewpoint claimed
> that averaging should be avoided near LAN.

Although this technique is similar to averaging it enables outliers
(statistics talk for, in our context, gross errors) to be eliminated,
thus an improvement on averaging that includes and is polluted by
them.

Take another look at "An example of a slope", 10 March 07.

Sights 1 and 3 have been discarded, as they cannot be matched to the
slope. This slope, a fact, is then best matched to the pattern of the
other sights that exhibit random error.

What is the alternative to this technique? In this example, taking
just the one sight could have been equivalent to choosing any one of
these sights at random. What were the odds of obtaining as good an
observation as the slope will produce with just the one sight?

Of a poor sight (#1&3):                      2 out of 9;         22%
Of a mediocre sight (#2,4,6,7,8,9):     6 out of 9;         67%
Of poor or mediocre:                         8 out of 9;         89%
Of an excellent sight (#5):                 1 out of 9;         11%

So at the cost of a little extra calculation and the drawing up of a
simple graph this 11% chance has been converted to a 100% chance of a
similar result to what appears to be the best sight of the bunch,
together with all the other advantages of KNOWING a lot more about
this round of sights, and being able to derive extra information (eg;
standard deviation) at will.

Is this a typical example? No. Typically there are less sights in the
5 minutes, and NONE of the individual sights is as good as the derived
slope; confirmed by comparing the resulting position lines to a known
position.

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