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Kieran:

You have applied your terms correctly.  ("You have been accurate.")

Where you say "consistency", you mean "precision", and your use of
"accuracy" fits the description of what you are applying it to.  Any
mathematical discussion of this is not possible without the actual numbers.
Then we could get into regression coefficients and so on.  Do we want to go
there??

In a nutshell, three terms have been reduced to two, which makes for better
understanding.  I run into this all the time while teaching GPS.  GPS is
relatively more accurate than LORAN-C, but its precision is far worse,
LORAN being a fixed system while GPS is dynamic.

Let's not open up the GPS discussion, but leave it at that.

John Kabel
London, Ontario

> 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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