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Thanks to Alex for posting his first set of six lunars, as copied below-

>I am posting the corrected table, including the
>rejected "blunder" observation which was not included in
>my earlier posting.
>Please notice: it was rejected BEFORE any reduction.
>I would always reject such an observation.
>I am waiting for your opinion whether my procedure was sound or not.
>
>AP: N 40d27.2'  W 86d55.8'
>GMT: 4:00 Oct 24, T=58F Pressure 29.75
>Observation from my balcony, height 12ft,
>Sextant SNO-T, index correction 0.0', inverting scope.
>One of the 6 observations (column 4) was immediately rejected
>because it did not follow the pattern of increasing
>distances. I reduced with Frank Reed's on-line calculator.
>First, each measurement, and then their average.
>The third line is the error in the distance, the fourth line
>is the error in the longitude:
>
>Moon-Altair:
>
>GMT   4:06:49    4:09:58     4:13:10  4:14:58   4:17:12    4:18:57
>DIST  51d22.2'   51d23.3'    51d23.8' 51d22.4'  51d24.1'   51d24.3'
>ERD       0.0'      +0.5'       +0.3'    -1.5'     -0.2'      -0.4'
>ERL      +0.3'     +13.5'       +8.7'   -44.0'     -7.3'     -12.2'
>
>After the rejection of column 4:
>AVERAGE GMT: 4:13:13  AVERAGE DIST: 23.54'
>ERROR IN DISTANCE: 0.0' ERROR IN LONG: 0.4'

Later, he wrote-

>But do you agree that that bad observation HAD to be rejected?
>It was evident to me immediately when I read my sextant.
>My reason and all what I know about statistics imply this.
>
>I suppose the reason of that blunder was incorrect time recording.
>My (easily solvable) problem is that I have no watch that I
>can read in the darkness and without eyeglasses.

===========================
===========================

Some comments from George-

Alex attributes the discordant point to a timing error, but I find that
hard to accept. Presumably, he noted his six observations in order, as they
were made, one after another. He might parhaps have recorded each on a
separate slip of paper, which were later jumbled, or jotted them at random
scattered over a piece of paper. Otherwise, they would presumably be in the
form of some sort of time-ordered list, noted down in sequence. Assuming
that observation 4 was otherwise precise, it would have required such an
error in timing as to make it, in truth, the second in the series, rather
than the fourth: which Alex couldn't fail to notice.

So, if they were listed in order, there has to be another explanation.

Perhaps something was different about that one observation. For example,
Alex might inadvertently have made his final adjustment to the sextant knob
anticlockwise, in the opposite direction to all the others. Sextant
backlash (= lost-motion) could then explain such a difference. He might
have been a bit less careful, on that occasion, about exact placing of the
star against the limb. Or he might have read, and written, 22.4' by
mistake, when it should really have been 23.4'; in which case it wouldn't
be seriously out of line with the others. I'm speculating, and we will
never know the answer.

Or possibly, the scatter in Alex's lunar distances is a bit larger than he
thinks it is. If the standard deviation was, say, 0.7', which is rather
good going, then his observation 4 would be out only by 2 standard
deviations (maybe less, depending on how you strike a "best line" through
the 6 points), and that's a statistical variation which is fully expected
in real-life.

One has to be very careful. By excluding the odd point or two out of a set,
it's often possible to draw a straight line through those that remain which
gives a spurious notion of precision. Alex will have a better idea than the
rest of us about the precision he now expects from each of his own lunar
distances.

What I'm getting round to saying, in a long-winded way, is that I rather
agree with Fred Hebard's point of view. Alex's point-4 may be classifiable
as a blunder, quite out-of-line with other observations, in which case it
could be plausibly rejected. Or it may be the result of statistical
scatter, in which case it should certainly be included. It's a borderline
situation, depending on one's judgment.

In a previous incarnation, I was an experimental physicist, and this has
left me with a strong prejudice in favour of including "odd" observations,
rather than rejecting them. And indeed examining them more closely, in case
they have anything to tell us. Rutherford's discovery of the atomic
nucleus, for example, hinged on such non-statistical scattering of alpha
particles. Not that I expect Alex's lunars to win him a Nobel prize!

If it was me, I would have included point-4. The resulting longitude,
averaging all six observations, would have given as answer a mean longitude
of 7' less than that of Alex's balcony: instead of 0.6' greater, as I make
it from averaging the remaining five. This would still be a remarkably good
result for a lunar, and something to be proud of.

However, I respect Alex's decision to remove point-4, even though I would
have done differently. There are valid arguments either way.

As a matter of interest, I ask Alex how he would have treated point-4 if
his observation happened to be 23.4' rather than 22.4'. It would still fail
his stated test, being out of a monotonic increasing sequence, so would he
then reject it automatically? I suggest that in that case it would be quite
wrong to do so.

Please don't think I am claiming to be any sort of pundit on the
measurement of lunars. My own sextant is a cheap plastic one, useless for
lunars even if good enough for other observations from a small craft. Where
I do claim some experience is in the treatment of observational errors.

George.

================================================================
contact George Huxtable by email at george@huxtable.u-net.com, by phone at
01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
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