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Re: Lunars with SNO-T
From: George Huxtable
Date: 2004 Oct 26, 15:59 +0100
From: George Huxtable
Date: 2004 Oct 26, 15:59 +0100
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. ================================================================