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I sent this post around just before Christmas in response to a listing from
Herbert Prinz. I had hoped for some comment on this matter and whether I am
on the right track. Could some of the mathematicians or statisticians on the
list oblige me?


Herbert,

I have been following the discussion in relation to applications of
line-of-best-fit to a series of lunar distance observations. Mention has
been made of the analysis I performed on lunar distance observations
undertaken by the Australian explorer/surveyor Augustus Gregory in 1856 (See
www.ld-DEADLINK-com for the paper written this subject). I am not a
mathematician and hesitate to tread such dangerous ground but there may be
some confusion between consistency, accuracy and precision in this ongoing
discussion.

When I applied the line of best fit technique to Gregory's analysis I was
trying to measure his consistency i.e. the deviation away from a line of
best fit. This says nothing about accuracy. To determine that I had to find
the actual location where the sights were performed  and compare this with
his computed location.

Alternately, as I now know his exact latitude and longitude  I could have
calculated the actual lunar distance at the time of the observations and
plotted these. This would have given a line which could be compared to the
line of best fit from the observations. Error would have shown  up in a
different slope to both lines.

To me these lines tell very different stories. A line of best fit applied to
a series of observations may be very consistent with a small standard
deviation and may be also very inaccurate not taking account of systematic
error such as shade error, incorrect calculation of index error, observer
bias, or failure to account for temperature and pressure. Thus a series of
observations may be consistent and also consistently wrong leading to a
wrong calculation of either GMT from a lunar or position from an astronomic
fix.

In Gregory's case the observations were both consistent and accurate but I
could not tell this just from a line of best fit of his observations.

The best explanation for the layman of laying an accurate line of best fit
to a series of observations and the use of altitude/azimuth diagrams in this
regard is in George Bennett's book, "The Complete On Board Celestial
Navigator".

Possibly some of the members more familiar with maths and statistics can
expand on the differences between accuracy, precision and consistency better
than myself.

Kieran Kelly

Sydney

Australia

   

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