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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Handling scatter
From: Andr�s Ruiz
Date: 2008 Jun 16, 12:22 +0200
From: Andr�s Ruiz
Date: 2008 Jun 16, 12:22 +0200
This paper, How to Average Celestial Sights for Optimum Accuracy, by David Burch can be found at: http://www.starpath.com/resources2/sight_average.pdf Andr�s -----Mensaje original----- De: NavList@fer3.com [mailto:NavList@fer3.com] En nombre de George Huxtable Enviado el: s�bado, 14 de junio de 2008 1:46 Para: NavList@fer3.com Asunto: [NavList 5430] Handling scatter. was [NavList 5421] Re: Exercise #12 Daylight Sun/Moon Fix Mike Burkes wrote (reassembled)- > I noticed a number of members averaged > the entire moon set but upon my graphing the set it becomes readily > apparent sites 21-01-40 and 21-03-22 are rejected therefore the line > of best fit falls nicely thru the remaining 6 sites and solving no 3, > the 21-00-48 site, yields an agreeable solution and a run-on sentence ======================= Response from George. I've made Jeremy's 8 Moon observations, being discussed here, available as an Excel attachment to illustrate the points involved. Mike Burkes has his own way of doing these things, but I suggest that the procedure he describes should not be copied. It may be of interest to the list to start a bit of discussion about methods of handling scatter, to discover the attitude of others, and Mike's message provides a good starting example. I will present my own views, which I like to think of as "scientific", to provoke some comment. I will go into this particular sight-reduction in some detail, not because it's an important matter in itself, but because it provides such an example of different approaches. I hope Mike isn't too sensitive to being used as an example in this way, and hope he'll argue back if he thinks fit. Jeremy has explained that the Moon limb was unsharp because the contrast with the bright sky background was very low, and therefore he was not confident about the precision of those lunar altitudes. Presumably, that uncertainty applied equally to each of the 8 observations, which show an unexpected amount of scatter. Mike wrote "but upon my graphing the set it becomes readily apparent sites 21-01-40 and 21-03-22 are rejected ...". Rejected by Mike, but on what grounds? In my view, the only valid reason for rejecting some sight from a set, and accepting others, is if it is so far out of line that it must have been the result of a blunder. If, on the other hand, it's the result of scatter due to difficult observing conditions, then one such observation is as good as any other, and the way to deal with the scatter is simply to average the lot, giving equal weight to every point. Because outliers are fewer in numbers than the main group, their contribution to the averaged result is correspondingly limited. However, if I were in a generous mood, I might be persuaded to go along with Mike's rejection of the very highest observation, made at 21:01:40, as being particularly far out of line with the rest, and perhaps plausibly the result of some sort of blunder; in which case I might reluctantly accept leaving that point out and averaging the rest. But what justification can he then offer for rejecting also the next-highest, at 23:01:22, while accepting the lowest, at 21:05:08? One is no further out-of-line with the rest of the group than is the other. But in the end Mike rejects much more than than. He looks at the six points that remain after discarding the highest two, and decides that on some basis he can draw a line through them, a line which happens to pass through the sight taken at 21:00:48. So he then discards everything else and works on the basis of that one point only. This process may have saved him a bit of arithmetic, in avoiding that averaging, but I suggest that a methodical averaging process would have squeezed the most out of the available information. As I side-issue, I've come across a procedure, adopted by some, when faced with the problem of reducing the scatter in a large number of observations of what ought to be the same thing, by doing the following- Reduce the range by rejecting both the highest and the lowest observation in the set, as a pair, before averaging the rest. Indeed, if there are sufficient observations, weed out the next remaing pair in the same way, and so on. In the extreme, this shifts the resulting answer towards the median of the set, rather than the mean. If the distribution is truly Gaussian, it does nothing to reduce the scatter, compared with simple averaging of the whole set; indeed, it increases it, though only slightly. The only virtue of this approach appears when the distribution is not truly Gaussian; if there are more outliers, further out from the average than ordinary statistics would predict (blunders, perhaps). Then a procedure such as this can provide a methodical way of weeding out such blunders. George. contact George Huxtable at george@huxtable.u-net.com or at +44 1865 820222 (from UK, 01865 820222) or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To , email NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---