NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Real accuracy of the method of lunar distances
From: Fred Hebard
Date: 2004 Jan 1, 16:40 -0500
From: Fred Hebard
Date: 2004 Jan 1, 16:40 -0500
Jan, I hope we're not bothering the list too much! I alluded to this key point of inferring the basic standard deviation from the mean values in my last post, sent just before your current post to which I am responding. In a one-way analysis of variance, the Mean Square for Error (within groups) would equal the error variance, in a components of variance model. The Mean Square for the model (among groups) would equal the error variance plus (the variance between groups multiplied by the mean sample size). I am assuming that there is no variance between groups, so that the two mean squares are equal, the F statistic is insignificant, and that either serves as a measure of error mean square. This is why I was previously alluding to increases or decreases in observer proficiency or drifts in sextant accuracy over the course of the voyage; these are the only factors of which I can conceive that would violate this assumption. I believe, though, that they would increase the "standard deviation" rather than decrease it, which would be OK for our purposes, as we are trying to put an upper bound on accuracy, not a lower bound. I've been looking at some of my own data, which include a few data sets others have sent in, to estimate this. I also suggested previously some tests you might try with Bolte's data set. Unfortunately, we have a social engagement to celebrate New Years, so I'm afraid I must desist from this interesting diversion for the time being. The one thing that throws me off in all this is knowing what the correct answer is! So I hope I haven't fouled things up here due to that. At any rate, Happy New Year! Fred On Jan 1, 2004, at 2:08 PM, Jan Kalivoda wrote: > Fred, > > Maybe we bother the list with the too detailed discussion already. But > it is easy to erase our postings, if needed, I hope. > > Nevertheless, to verify your point of view, one would need to know the > standard deviation of the basic sets of six measurements. We can > suppose that it was stable throughout all the period of observations, > as you say, but we don't have the data for each measurement to > ascertain it, we have the data only for the means from each set of six > measurements. But you state that it is possible to deduce the standard > deviation you need from the variance of the whole series of the means > - without giving any details.