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Re: Data Processing (1) - further thoughts

On Wed, 29 Dec 1999 09:15:15 +0000, Martin Nicholson <Martin@crozet.demon.co.uk> wrote:
*>In message <199912281901.OAA00720@a188-l009.rit.edu>, Stupendous Man
*><richmond@a188-l009.rit.edu> writes
*>>  No, probably not.  The measurements in the Mark III database 
*>>have uncertainties which are quite large (compared to many past
*>>surveys of stellar brightness).  The brightest stars have a 
*>>typical standard deviation of about 0.03 mag; that means that
*>>a _constant_ star, one which was always exactly mag V = 8.00,
*>>would appear in our database with numbers like this:
*>>          7.99, 8.03, 8.01, 8.00, 7.97, 8.01,   etc.
*>>  The uncertainties in the Mark III measurements increase with stellar
*>>faintness.  If you look in Technical Note 56, specifically at
*>>    http://a188-L009.rit.edu/tass/technotes/tn0056.html#photometry
*>>you'll see a table and a graph which list the median of standard
*>>deviation for stars in the database.  

Incidently, one would expect larger variation with dimness, if only
because the noise due to the background and due to dark current becomes
more signifigant. Not to mention sky conditions.

*>>  Only stars which have a standard deviation larger -- say, three times --
*>>than the median standard deviation, should be considered good 
*>>candidates for variability.  For example, the table shows that
*>>at mag V = 10.00, the median standard deviation is about 0.046 mag.
*>>Thus, a star with standard deviation, say, 3 * 0.046 mag = 0.15 mag,
*>>might be a good candidate for further research.
*>>                                                 Michael Richmond

I suspect that Richmond is suggesting "3 standard deviations" strictly
from statistics. That is, at 3 st. dev. it is unlikely that the deviations
are due to chance, as I recall up to over 95%, look it up. But keep in mind
this is stars, not dice: there are many definitions of a variable star, depending
on its observable characteristics as well as the presumed physics of the

*>I have now examined the 68 stars (in the region RA 100-200) where there
*>is a match between a TASS star and an identified variable in the GCVS.

...and what are the characteristics of those stars? THAT should define
what you are searching for, if you question is how the TASS survey
best represents these stars. Does star #1 vary by .5 mag in the GCVS -
and do the TASS measurement reflect that variability? Or can you class
them by variability: .5 mag, 1.0 mag, etc.?

*>Of the 68 -
*>18 had a SD less than the median value in TN56
*>50 had a SD greater than the median
*>Of these 50 -
*>32 had a SD greater than twice the median
*>11 had a SD greater than three times the median
*>This means that if I confined my study to those stars >3 times the
*>median value I would only find 16% of the known variables.

I don't understand what "median value" means, in this or your previous
note. A median value of standard deviations of a group of observations,
if that is your meaning, strikes me as an uneven indicator of anything.
With TASS, Richmond says in effect "I took the observations of three
sites with similar equipment, made some corrections, and put them in
a database if we had more than X different observations from Y sites
and filtered cameras." Examine his report to see what the "input"
uncertainty is (per observation) versus the "output" uncertainty
(across the databased observations).

What is a variable? It is a star with a varying value. It is NOT a
star that has a given uncertainty of measurement. I can measure a variable
and have uncertainty for each measurement, but hopefully its variability
exceeds the uncertainty!

*>This is not of course to say that SD is not a useful indicator of stars
*>to study, far from it, simply that taken on its own it is too crude. Not
*>least because some of the stars with a very high SD have one rogue point
*>spoiling an otherwise straight line.
*>Martin Nicholson

...which is a way of saying that standard deviation of ALL the measurements
is not necessarily the st. dev. of each measurement. The st. dev. of each
measurement is based on its comparisons to other stars as measured on
the image of the evening, probably thousands of stars. The st. dev. of ALL
the measurements for that item in the database (and hopefully in the
sky) simply represents the spread of those recorded measurements, probably
TENS of them: therefore it is less reliable as you suggest, one outlyer
out of ten will throw it.

My point in my comments is that it is important to keep in mind the physics
and the data collection process involved with the TASS database items. As
you yourself conclude, raw statistical analysis can be misleading. But as
you have some actual variable data in hand, and the corresponding TASS
observations of them in hand, it would be VERY INTERESTING to compare
them one-for-one, object for object; I hope you do so.

I myself find that TASS is a great opportunity to learn real statistics,
so I appreciate a chance to work these issues. I hope my remarks are
correct and not misleading.

Herb JOhnson

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