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    Re: errors in plotting and a possible/partial fix thereof, as menti...
    From: Peter Fogg
    Date: 2010 Dec 30, 13:45 +1100
     George Huxtable wrote:
    Is Peter Fogg really claiming that he has a method which can reduce the
    error resulting from random scatter to less than simple averaging will do?
    Yes or no? If so, I can always produce sets of simulated data, which are
    affected only by computer-generated random scatter, on which he can try his
    magic, to substantiate that claim.

    First of all, its not my magic.  The method could well have been reinvented a few times, as it is proposed by different navigational gurus (eg; David Burch, George Bennett, etc) who may or may not have derived it from the same source. Which reminds me -  Byron Franklin did apparently reinvent and present it here not so long ago.  I was impressed by that, Byron, and I am similarly impressed by your other techniques shown here.  There is little truly new but reinventing something you are unaware of merits the same respect due to the original inventor.

    Next to George's "simulated data".  We have seen examples of your carefully contrived examples before, have we not George?  You have, on more than one occasion, and in dealings with different people and matters, gone to what must have been considerable effort on your part to find some data set to 'disprove' some procedure or other. 

    In the past, as I expect you remember well, no little counter-effort was required to be expended, and was expended, in order to conclusively show that the proportion of data sets which gave a counter-indicative result was truly minuscule, and of no practical significance.  Remember?  Its all in our archives. 

    This is not good science, George, this is mischief-making.  It is also intellectually dishonest, as I expect you remember me pointing out already.

    If you want an example from the real world I have (re)provided this quite recently.  Remember?  Some poor, some mediocre and one excellent sight that was derived from a set of 9 sights via use of the slope method.  I expect that if you ever climbed out of your navigational armchair and actually put the technique to the test, actually used it, then you would be able to supply your own examples and answer your own criticisms.  No computers needed.

    But this is one thing that you will not do, is it not George?  You prefer to refuse to consider the possibility that there might be some merit to the technique while having no practical experience of it.  Is this not so?

    It kinda begs the question of just why you are so hostile to a proposed method that you refuse to actually try.  This seems irrational, which is probably the kindest thing that can be said about your behaviour on this issue and others you take a shine against. In this case, I may add, without producing any evidence of your own to discredit the method, apart from what I suspect is your current kind offer to concoct some.

    Having said all of that, and assuming for the sake of the argument that you were not intellectually dishonest, your proposed methodology appears flawed.  If you produce "sets of simulated data, which are affected only by computer-generated random scatter"  then there may well not be any pattern to the sights which more or less should follow the actual slope. If this is what you are proposing; a quite unrealistic scenario, then of course the method won't work.

    In this case your computer (I did learn once to do this with a calculator but am more than a little out of practice) can derive a line from random data. This is linear regression. The very pertinent question, though, is whether this derived line is likely to be of any navigational use?  Only if it is the same as the actual slope of the body's apparent rise or fall. Why would it be the same except, assuming random error is present, by unlikely coincidence?

    Regularly people here do propose linear regression as a method of averaging, which it is.  But its the wrong tool for this job.  Wrong  because it will, unless the data set is so good that no analysis is required, produce the wrong slope.

    Even if the data set is very good, use of slope could still be worthwhile, as you are provided with a picture of your sights to compare with the actual slope.  If all of the sights are as good as they were in Antoine's recent sample then you could as well pick any of them - BUT- you will have the advantage of knowing how good, or not, the sights are because the picture will be clear.  Averaging doesn't provide this assurance, its just blind number-crunching.

    I understood that his reason for declining such trials, when last offered,
    was that that his procedures could not be expected to improve on such
    Gaussian scatter, but could only improve on non-Gaussian outliers.

    Here you've lost me.  You seem to be using "Gaussian" and "non-Gaussian" in some sense that is not clear to me.  Try again in plain English.

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