[Aavso-photometry] Uncertainty of Averaged photometric measurements

[Brad Walter]

Further to Michael Newberry's response. There is a very good paper
describing the correlation of noise between photometric measurements taken
from a time sequence of images. It isn't too hard slogging, and it gives
practical means of calculating the noise reduction you actually achieve from
averaging images. The paper is "The effect of red noise on planetary transit
detection" by Frederic Pont, Shay Zucker, and Didier Queloz. You can get it
here: http://arxiv.org/abs/astro-ph/0608597.

The bottom line is that the brighter the star, the more correlation there is
between noise on images taken in a given interval of time, and it can be
much harder to really get those millimag errors than the 1/SQRT(n) formula
predicts.   


------------------------------

Message: 4
Date: Mon, 19 Nov 2007 19:30:29 -0700
From: "Michael Newberry" <mnewberry at mirametrics.com>
Subject: Re: [Aavso-photometry] Uncertainty
To: "Richard Harvan" <tkdvarstar at yahoo.com>,	"AAVSO Photometry"
	<aavso-photometry at mira.aavso.org>
Message-ID: <E25E13EF35754B24B7C68661B89D1261 at Serrano>
Content-Type: text/plain; format=flowed; charset="iso-8859-1";
	reply-type=original

Hi Richard,

What you describe in the first paragraph is reasonable.

What you describe in the second paragraph is also correct, but you need to
be careful about what you use for "n" in the square too. Also note that this
formula for the "error of the mean" gives the least possible statistical
error (the "internal error"), and measurements (especially in astronomy)
include sources of "external error" that you haven't accounted for in such a
calculation. The value of n would be the number of independent estiamtes you
are combining. For example, if you measured the star on 10 different frames,
then n would be 10 and the error in the average magnitude you derive from 10
frames estimate from 10 frames would be about 3 times better (that is 1/3
the uncertainty) of what you would get from 1 frame. However, to be able to
combine measurements on different frames, you have to believe that the
individual matnitude measurements do not vary between frames in some
systematic way---otherwise the statistical assumptions that allow you to
combine estimates and beat down the random error by sqrt(n) do not apply.

Michael Newberry

----- Original Message -----
From: "Richard Harvan" <tkdvarstar at yahoo.com>
To: "AAVSO Photometry" <aavso-photometry at mira.aavso.org>
Sent: Monday, November 19, 2007 6:55 PM
Subject: [Aavso-photometry] Uncertainty


> Dear All,
>          I would like to get your opinion on my calculation of 
> uncertainty.  The procedure I am writing about calculates the standard 
> deviation of the variable and the check star.  These values are then 
> combined in quadrature with the stated uncertainty of the photometry of 
> the comp star and check star.  Is this a reasonable method or am I going 
> overboard.
>                    I saw in a textbook that the uncertainty of an average 
> was the standard deviation divided by the square root of the sample size. 
> When I applied this to my data the calculated value was much less than the

> stated uncertainty.  This seemed too good to be true, so I have doubts 
> about applying this to my measurements.  What is your opinion?
>  Thanks for your help in advance.
>
>  Rich Harvan
>
>
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