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    Re: Averaging
    From: Chuck Taylor
    Date: 2004 Oct 20, 09:37 -0700

    --- Herbert Prinz  wrote:
    > If Peter has in mind a simple visual approach with
    > paper and pencil when he
    > speaks of "best fit", I can accept that. But
    > bringing Microsoft into this stage
    > of the sight reduction game is a severe faux pas.
    Microsoft Excel is simply another tool, like pencil
    and paper.  Some people find it easier to make a
    simple plot with a spreadsheet than with pencil and
    paper, and I think that is what Peter and Jim were
    Herbert goes on to say:
    > The US Power Squadron recommends (in fact demands
    > for the sight folder to be
    > submitted for graduation from the JN course) that
    > every altitude sight be
    > repeated at least three times and be checked for
    > 'consistency'. Such a group of
    > sights the call a 'run'. (Junior Navigation, 99/01,
    > p. 2-11 and Appendix G)
    > They specify what 'consistency' means: A rising body
    > must show a steady growth
    > in altitude, a setting body a steady decrease. The
    > consistency rule is waved for
    > sights near the meridian. (N.B. Alexandre: Altitudes
    > above 75 deg are
    > discouraged, but admitted!).
    I am a member of the national USPS (United States
    Power Squadrons) committee that oversees the Junior
    Navigation and Navigation courses, and have been
    teaching both courses and grading USPS sight folders
    for I-don't-remember-how-many years.  High-altitude
    sights are admitted for the Navigation course, but not
    for the Junior Navigation course.  The same applies to
    low-altitude sights (below 15 degrees), because
    temperature and barometric pressure corrections are
    not taught until the Navigation course.
    > In the USPS course, averaging the sights within a
    > run is an option. One is
    > supposed to record all sights in a log (Form ED-SL
    > (98)) and enumerate them. The
    > instructions on the back of the form say that for
    > the reduction you can either
    > pick one sight from a run, or average several ones.
    > The only guidance given is
    > to dismiss obviously 'inconsistent' sights.
    This is not so.  One run of 5 averaged sights is
    required for the Navigation course, but averaged
    sights are not otherwise admitted.  USPS teaches sight
    averaging as one technique for compensating for random
    error such as might occur on a small-ish sailboat in
    rough weather.  The instructions cited on the back of
    the form refer to the one instance in which averaging
    is required, and not to any run.  (I have just re-read
    those instructions to be sure.)
    Herbert went on to discuss the appropriateness of
    fitting observed altitudes with linear models.
    > First, the altitude grows in a linear fashion near
    > the prime vertical. There,
    > you would use linear regression. Near the meridian
    > you would have to use a
    > parabolic fit. That's also easy. But what kind of a
    > fit do use in-between? ...
    I am reminded of the words of a famous statistician by
    the name of Oscar Kempthorne, who taught at Iowa State
    University:  "All models are wrong; some are useful."
    Certainly a straight-line fit, whether by eyeball or
    by linear regression, is not rigorously correct in
    this situation.  Still, within appropriate limits, it
    is useful for highlighting possible outliers.  As
    Kempthorne pointed out, a good statistician does not
    necessarily *believe* his or her model.
    Standard procedure for plotting a line of position
    using the St. Hilaire method calls for plotting a
    straight line, when we know that what we "should" be
    plotting is the arc of a great circle.  Still, the
    straight line is useful.
    Chuck Taylor
     47d 55' N
    122d 11' W
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