NavList:

Frank, thanks for your explanation; it’s reassuring to read that plotting altitude as a function of time is all one needs to do when analyzing a run of sextant sights, as other factors (changes in declination and parallax) are included “for free”, and that changes in azimuth don’t matter.  It’s always very appealing to get something without any extra effort!

You wrote: “The difference from a straight line [in the plot of altitude as a function of time you included] would seem to be everything that you were asking about in your original post, and that's what I tried to address. But now you say that it's not what you meant. What are you asking then?”  Perhaps I did not make my initial question clear enough, but that was not my point.  My query only concerned which variables one needs to consider when reducing a set of  altitude values.  However, I was very interested in your result on how much the exact altitude - calculated from changes in Sun coordinates and the geometry of the sky - would differ from an altitude given by a simpler straight line fit.  The difference between them, though not very large (about 1’ by your analysis), is larger than I thought it would be.  Obtaining a shorter run of measurements seems a simple and elegant way to reduce this difference, and I’m planning to adopt this approach in the future.  Also, calculating an “averaged" sight by averaging (Ho - Hc) intercept values looks like an intresting project. I’ve placed a bookmark on the appropriate page of my 2023 (and last?) orange-covered edition of the Nautical Almanac.

Regarding outlier values, my impression is that the only measurements which one may reasonably discard are those that are so large that they are far more likely to be the result of a careless mistake than due to a measurement fluctuation. This may be a somewhat circular argument, but I think it’s still a useful sanity check, appropriate for practical purposes.  Beyond these large discrepancies, to answer your questions “how big is too big?” and “what qualifies as clearly abnormal?", I don’t see any way out other than a statistical approach: decide what degree of error you agree to tolerate when accepting or rejecting a given measurement, based on probability criteria.  And I agree, it’s fascinating to reflect on how many topics in science, mathematics, and statistics have been motivated by positional astronomy and its applications for nautical astronomy.

Best, Rafael