NavList:

Rafael, you wrote:
"first I would like to return to my original question, which was whether I should account for the fact that the Sun’s azimuth and declination were changing"

I didn't spell it out, but my point is that it's all included "for free" if you just calculate the altitude as a function of time. It doesn't matter "where it comes from". Does the changing declination enter in? Yes, sure, but we don't have to be explicit about it. How about the changing parallax in altitude of the Sun. It's 9 seconds of arc at the horizon, zero at the zenith, so it's falling with the increasing altitude of the Sun. We don't have to include that explicitly either, but nearly any tool you use to calculate the true altitude of the Sun during a run of sights will incorporate that changing value anyway ..."for free". As for azimuth, what are you picturing? If you're plotting altitude versus time, azimuth just doesn't matter. You could do a different plot of altitude versus azimuth, but it doesn't offer any advantages here.

You also wrote:
"Since you do not mention that any compensation is required, I interpret this as meaning that you think that the effect these changes is irrelevant for this relatively short interval of less than 30 minutes."

No, I meant that you don't have to do any additional or any explicit compensation. It's in there!

And:
"Second, the main reason why I prefer to collect more than one single altitude measurement is to do what you mentioned, to reduce the “noise” in my sights by including more measurements.  I use a standard approach to analyze these data points: fitting them with a line (a straight line or a curve) that approximates their behavior, by means of a standard graphing software package. Although the line that describes the sun’s apparent motion in the sky is slightly convex, as you point out correctly, in a summer morning at my mid-latitude this convexity was very modest, and a straight line seemed good enough for the practical purpose of minimizing the “wobble” due to my imperfect measurements. I do understand that a straight line isn’t an accurate physical model of the sun’s apparent motion; this becomes quite obvious as the sun approaches the meridian."

The difference from a straight line 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?

You wrote:
"I’m afraid that my mention of outlier values wasn’t clear enough."

I thought your description was perfectly clear, and I was simply asking you to elaborate on the idea... you know... to continue the conversation! ...since that's what we do. 

You continued:
"Another reason why I like to collect a set of altitude measurements is just to make sure I haven't made any outrageous mistakes, such as reading the wrong degree value off the sextant’s arc, or jotting down a wrong number. This would show up as a flagrant outlier jut using the “eyeball test”. I did not mention any formal way to eliminate outlier values, because I haven't used one."

The question then is just this: what qualifies as an "outrageous" or "flagrant" mistake? How big is too big?

You wrote:
"I recall that a formal method to identify outliers in linear regression is to use Cook’s distances. A statistician friend (American school, no doubt) introduced me to this approach, which I haven’t used since my retirement. If memory serves, it involves calculating a regression line with and without each point of the data set in succession. A rule of thumb, according to this statistician, is that a point which has a Cook’s distance three times the mean of all distances may be labeled as an outlier. But, as I’ve said, this is beyond the scope of my far more simple-minded approach."

Sure, that's for formal papers. Also Peirce's criterion and Chauvenet's criterion. I mention these latter two formal rules only because they are exemplars of the American school on this topic, and two names deeply connected with the history of nautical astronomy. Sextant observations are the start of all of this! 

But formal rules for formal papers are nothing we have to worry about, right? We can ask, what should we do in practice. In practice, your eyeball test is probably something similar to Cook's rule but less wordy. You have a general idea of the "normal" scatter in your observations, right? It's maybe +/-1.0 minutes of arc by standard deviation (meaning that roughly two-thirds of observations are within that limit of a central mean). Then a sight comes along, and it's out by 30 minutes of arc. Well, that's certainly a "flagrant" outlier! Be gone outlier!! And zap, it is forgotten :). But is it flagrant at 4 minutes of arc? How about 2.5 minutes of arc? That's an interesting question, right? If you look at the "normal" scatter of your sights, what qualifies as clearly "abnormal"? They don't come with labels [unlike abnormal brains :) ].

Frank Reed