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On Sep 24, 2015, at 12:07 PM, Frank Reed <NoReply_FrankReed@fer3.com> wrote:

Peter Fogg, you wrote:
"Yes. Finally. Sanity has prevailed."

Don't forget that many of us agreed with your advocacy of a system for analyzing outliers based on plotting. It remains a somewhat contentious idea in some quarters because, from the point of view of certain philosophies of statistics, one should never throw out any outliers in a data set since the idea of identifying bad points is fraught with observer bias. And in general, that's true. But the manual process of celestial navigation sights is different from many other types of data collection. Outliers that fall more than three standard deviations from the mean of a set of observations are much more common than a normal distribution would allow, and that implies both that they can detected under the right circumstances and also that removing those points improves the results of averaging. And that's the whole point.

In the late 19th century, when Chauvenet (a highly-respected American mathematician) proposed a statistical test for astronomical observations (not navigators, but professional observers working in observatories) that could be used to cull outliers from a set of observational data, his methodology was supposedly scorned by many European (continental) mathematicians. It's a rare, interesting case where a cultural attitude played a role in a mathematical discussion. 

Frank Reed