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Fred & Jan,

With apologies for butting into your exchange but you two seem to be
misunderstanding one another:

Fred: What you are suggesting is, I think, a paired-comparison t-test of
the null hypothesis that the mean of all possible positions estimated by
lunars is not different from the mean of all possible positions
estimated by chronometer, using a sample of paired position estimates,
one each by lunar and chronometer (where, of course, each "estimate" is
actually based on multiple sextant observations on the same day). That
would be one way to see whether there was a bias in the lunar estimates
of position but it would not address Jan's interest in the average
absolute magnitude of the differences between the lunar and chronometer
estimates.

For that, Jan already has someone else's estimate of the "probable
error", meaning the absolute difference that will be exceeded by 50% of
paired position estimates (on average). To get from that value to the
standard deviation of the errors in the lunars, he has assumed that the
chronometer positions are exact (which is likely close enough to the
truth) and has consulted the percentage points of the _Normal_
distribution, _not_ the t-distribution which you turned to. Armed with
the standard deviation, he has again turned to the Normal distribution
to read off the error that should occur in 3 estimates in every thousand
(i.e. 1-0.997 = 0.003 of lunar estimates).


The problem with that, as I have noted in earlier messages, is that the
errors in the lunars are unlikely to be exactly Normally distributed.
Otherwise, I think that Jan has followed the right path in trying to
estimate the magnitude of the errors that a skilled navigator might get
with lunars. He doesn't need hypothesis testing and hence he does not
need the t or F distributions.


Trevor Kenchington


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Trevor J. Kenchington PhD                         Gadus@iStar.ca
Gadus Associates,                                 Office(902) 889-9250
R.R.#1, Musquodoboit Harbour,                     Fax   (902) 889-9251
Nova Scotia  B0J 2L0, CANADA                      Home  (902) 889-3555

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