[Aavso-photometry] Ensemble photometry question

[arne]

You "win" in ensemble because you are dealing with an error of the
mean, not an error of a single measure.  So you get to divide by
(N*(N-1)) in the denominator before taking the square root (assuming
all comp stars have unit weight).  See the statistics chapter in
Henden and Kaitchuck.  In other words, even though each star in
the ensemble has some error, the average of the ensemble is known
to much greater precision.

Once you have the error of the ensemble, then you need to take that
and add in quadrature with the error of the target star.  The goal
is to end up with pretty much just the error of the target star, with
the comp/ensemble error being a negligible extra contribution.

Statistics sounds complex, but really isn't at this basic level.
A lot of it is differences in terminology between what astronomers
use, what computer scientists use, and how mathematicians describe it.
Arne

Robert J. Modic wrote:
> Thanks Pertti and Arne.  Let me clarify what I'm trying to 
> do.  I already know the errors of each comp star (taken from 
> one of Arne's .dat files for example).  I'm just trying to 
> calculate the portion of the error due to the ensemble of 
> comp stars.  Adding all the errors in quadrature results in 
> an error that is too large.  I then tried dividing the previous 
> result by the square root of number of stars used.  This gives 
> an error that is very close to a simple average of all the 
> comp star errors.  Since the error should be reduced by the 
> square root of the number of comp stars, the result of this 
> second method still seemed too large.  The only way I can 
> calculate an error that looks right is to add all the errors in 
> quadrature and then divide this by the number of comp stars
> (not the square root of the number).
> 
> I read the Honeycutt paper on ensemble photometry.  The
> methods mentioned in that paper are meant for a non-homogenous
> set of comp stars and seem too complicated for the more
> simple type of homogenous ensemble photometry that I'm trying
> to do.
> 
> Again, I'm just trying to find a simple way to calculate the 
> component of the error due to the comp stars (the zero point
> error).  This will then be added in quadrature to the other
> errors (measurement, transformation, etc.) to get my total
> error for each magnitude measurement.
> 
> Bob
> 
> 
> 
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