NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Taking four stars for checking accuracy of fix - and "Cocked Hats"
From: Peter Fogg
Date: 2008 Aug 4, 04:21 +1000
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From: Peter Fogg
Date: 2008 Aug 4, 04:21 +1000
George wrote:
I'm glad you said that, as its something I've always wondered about this averaging idea.
No. You still don't get it, George. You have to THINK about the scatter of those points. You need to weigh this data evidence, then distribute weighting judiciously. You need to free your mind from this straitjacket of statistical averaging.
Once again, you really need to be in the position of having used the process in order to be able to make this assertion. An assertion based on what, apart from your theorising?
If magic you require then the simple elimination of outliers (gross error) is magic enough, I suppose. What you don't seem to understand is that all sights, unlike men, are not created equally. Some are better than others. The HUGE disadvantage of your blind statistical process is that it can only treat them all equally. Have you grasped the point about how just one gross error can drag the average well away from a nice little pattern that hugs the slope?
Yes, it's better to calculate the slope thanc trying to determine the slope
of the fitted straight line from the data points themselves; no question
about that. And it's better than simply averaging those changing altitudes
over the time period, if the observations were unequally-spaced in time. (If
they were equally spaced, you would arrive at exactly the same answer).
I'm glad you said that, as its something I've always wondered about this averaging idea.
But having done that, all that's been done is to compensate for the known
steady rate of rise or fall. And it's done nothing to reduce the statistical
scatter of the points about that line. You raise or lower that line, with
that slope, until it runs between your points, as centrally as possible.
No. You still don't get it, George. You have to THINK about the scatter of those points. You need to weigh this data evidence, then distribute weighting judiciously. You need to free your mind from this straitjacket of statistical averaging.
And
the uncertainty in getting that best fit, by eye, is no better (but may not
be significantly worse) than when tackling the same problem at the moment of
a meridian passage, when the altitude is unchanging, and simple averaging of
all sights gives the best answer.
Once again, you really need to be in the position of having used the process in order to be able to make this assertion. An assertion based on what, apart from your theorising?
There's no magic process of eliminating
the random scatter. It remains the scatter in each single observation,
divided by the square root of the number of observations.
If magic you require then the simple elimination of outliers (gross error) is magic enough, I suppose. What you don't seem to understand is that all sights, unlike men, are not created equally. Some are better than others. The HUGE disadvantage of your blind statistical process is that it can only treat them all equally. Have you grasped the point about how just one gross error can drag the average well away from a nice little pattern that hugs the slope?
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