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Alex,

Comments below.

Fred

On Sep 30, 2004, at 7:38 PM, Alexandre Eremenko wrote:

> Dear Fred,
> There are several points in your message I want to reply:
>
> On Thu, 30 Sep 2004, Fred Hebard wrote:
>
>> It's only recently that my
>> standard deviations have started coming in consistently under 0.2'
>
> As a mathematician, I don't like the standard deviation
> for suich small samples.
>
> What I do with multiple observations is this:
> 1) first I plot the measured altitudes against time
> and see whether the dots are on the straight line.
> Usually most of the points fit a straight line well,
> with one, sometimes two relatively much off.
>
> Those which are clearly off the line should be discarded.
> They can be off only because of some mistake in the
> measurement or recording.
>
> The rest I average and then reduce the average.
> I mean this is what I would do in a "practical situation".
>
> In my current experiments, I reduce all observations,
> (except those rejected). Then obtain the average deviation,
> and for each observation compute the difference
> between the deviation derived from this observation and
> the average deviation.
>
> Then I consider the MAXIMAL difference as a measure of
> quality of my measurement.
>
> Something like this is recommended in several books.

The standard deviation I am computing is the standard deviation of (Ho
- Hc) around its mean.  So it's somewhat similar to what you describe.
The word deviation is being used in two senses here.  First,  where (Ho
- Hc) is a deviation, and second where I compute the standard deviation
of (Ho - Hc).

I generally do not reject data points for altitude shots as you
describe, although I have for lunars.  Especially for night altitude
shots where multiple bodies are observed, I have found for me that
three observations of each is best, in order to avoid getting too tired
observing the first few bodies.

I expect either your method or mine would give one a metric of the
precision of the data by which improvement in one's technique could be
assessed over time; I certainly recognize that the standard deviation
of 3-6 replications could be highly variable .

I have no idea about the statistical properties and desirability of one
method over the other.

> I don't like this because then I have to reset the stopwatch
> for each observation. (besides, I do not have a stopwatch:-)
> At the moment
> of contact,
> I say "Yes!" to myself (aloud) then quietly turn my face
> from the sextant to the watch, and look at the seconds first.
> Then I subtract one second (needed to say "Yes!" and turn my face).
> And record seconds first, then minutes then hour.
>
>> to record to the tenth of a second, which I haven't done thus far.
>
> Do you really think this may have any influence on your
> result? Let us count: 0.1sec=1.5"=0.025' and we agreed that
> a sextant scale can be read only up to 0.1'.
> So it seems that the tenths of a second are irrelevant.
>
> The Russian manual recommends to record the time to 0.5
> of a second
> though:-)

I use the stopwatch built into my $20 digital watch, setting it to
Greenwich time as indicated by the computer, which synchronizes over
the internet.  I am not sure about the UT UT1 business there; I plan on
getting a radio, but have not done so yet.  The stopwatch has a button
that will stop the display, then when you press it again, the watch
jumps to the total elapsed time since it was started.  So it needn't be
reset between observations, although if you press the wrong button and
reset it completely, you're out of luck.

For the sights I reported earlier this night, each tenth of a second
gave about 0.02' increment in arc.  So one could be in error by up to
0.1' of arc rounding to a second.  It's easy to record to a tenth of a
second using a digital stopwatch.  It would be impossible without a
stopwatch for one person, in my opinion.  I'm sure there would be a
consistent systematic error associated with starting the stopwatch
imprecisely.

Timing to this accuracy would be unnecessary if, in my measure, the
standard deviation of observations was well over 0.2' of arc.

   

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