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Frank Reed wrote:

>It's "logical", sure. But that doesn't mean it's the whole story, or right.
>
>I think it's easier to understand why the calculated slope works if
>you start with the navigator's "normal" method for throwing out
>outliers, namely working up the sights and plotting them.

Thanks for your patient explanation Frank - I understand what you are
trying to say, I was just being "picky".

I had an interesting experience on one of my desert trips when trying
to nail an altitude for Polaris. Perhaps I had had too much gin &
tonic as the sun was going down, or perhaps it was the heat rising
off the plateau just to the North of the camp site, or perhaps
Polaris was not as bright that night, but I was getting an unusually
large variation in altitudes from the series of  sightings. So,
instead of the usual five sights, I ended up taking 20 sightings of
Polaris. I went on to take a round of sights of other stars and their
altitudes were no trouble at all.

Anyway, I found that the averaged Polaris LOP was closest to the
intersect of the other LOPs provided I averaged ALL the sights and
did not throw out any "outliers".

I think the lesson here was (or at least, the lesson I drew from it
was) that throwing out outliers is fine, if there is some systematic
- ie non-random - reason for them being outliers. And let's face,
there is often a slip in the arithmetic or a mis-reading of the
watch, or the sextant, or some darned thing. In this particular case,
there was some effect which was increasing the random spread of my
Polaris sightings, and the answer was not to make the statistics even
worse by throwing some of the sights out, but to improve the
statistics by taking more sights and getting a better average.

So, I am wary of throwing out outliers as a matter of routine. If
they are random and sitting on the skirts of the Gaussian spread, it
might be best to keep them in  - and if keeping them in makes that
much difference, I should have taken more sightings to reduce the
error on the average.

Having said all that, I will now go and read Chauvenet and see what
he has to say. Trouble is, my Googlebook Chauvenet is difficult to
navigate, as he has a tendency to refer to other bits of working
hither and thither - which is fine if you have the real live book in
your hands and can quickly thumb through it, but not so fine with the
electronic version.


Geoffrey

   

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