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Kieran,

I believe you are using consistency in the meaning usually reserved for
precision.  Essentially, precision is the repeatability of the
measurements.  As you indicated, it is separate from accuracy, which is
how close your measurements conform to the accepted value.

I am not enough of a statistician to address these issues more than the
above.

Fred

On Dec 29, 2003, at 9:19 PM, Kieran Kelly wrote:

> 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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