[Aavso-photometry] When to submit "Fainter Than"versusactualnumbers.

[Jeff Hopkins]

Hello Geir,

Thanks for the continued explanation of what you are doing.

As I mentioned in the last message a check star is used as a safety. 
It is normally used like a comparison star and subtracted from the 
program star just like when the comparison is subtracted from the 
program star.  I've never seen the check subtracted from the 
comparison. If you are using this third star as something else, that 
is new to me, but I would advise caution in doing so. It may 
introduce more errors than it helps.

I recommend that you take your 100 images and group them in sets of 
three adjacent measurements. Best use 102 or 99 images (a multiple of 
three).  Take the three resulting program star magnitudes and average 
them. Then determine the standard deviation for that set of three. 
The standard deviation then reflects on how close the grouping of the 
three measurements are. Otherwise just a single value gives no hint 
as to any variation. This is how I've always seen it done and the way 
I have been doing it for over 25 years.

One may wonder what value a standard deviation is for a sample 
population of only three values. While it is true the larger the 
population (more values to be averaged) will produce a more 
meaningful standard deviation, a minimum of three values can still be 
very useful and does provide a good indication on the quality of they 
data. Naturally you cannot take a standard deviation on just one 
value and two values is better the three is really the minimum that 
can be used and be significant.

Again on precision, think of your computer clock. You write a program 
to time an event to a micro second. The event displays a time of 
2.321379 seconds. You have a precision to 6 places, but what is the 
accuracy? It may turn out your clock oscillator has drifted and the 
real time interval was 1.987334 seconds. While you displayed a high 
precision the accuracy is horrible and of little or no value.

Jeff

At 02:02 -0700 1/28/05, Geir Klingenberg wrote:

>What I am saying (or trying to say) is nothing new, it is just what
>Michael and Gary described. I am sorry if something got lost in
>translation (I am Norwegian), but I think the only thing we disagree
>on is how to estimate the measurement uncertainty.
>
>For example, say I have say 100 images from a time series run. For
>each image I then measure
>
>X = V - C
>Y = K - C
>
>V, C and K are the instrumental magnitudes of the target, comp and
>check star respectively (I assume only one comp star for simplicity).
>Since I don't transform to a standard system I simply add the comp
>stars catalogue value to X to get the final estimate of the target
>star magnitude for each of the 100 images. I believe this is all
>pretty normal differential photometry.
>
>Now for the uncertainty. There is a measurement uncertainty for each
>of the 100 data points and it will in general vary from point to point
>due to bad tracking, changing sky conditions etc. It is common to
>estimate uncertainty based on SNR but this has shown to be too
>optimistic. Instead one could average say 5 and 5 subsequent
>measurements and use the resulting 20 measurements as the final data
>set. One could then use the standard deviation of the five
>measurements in each average as the uncertainty, but this is on behalf
>of time resolution. The standard deviation of the total 100 target
>star measurements can not be used since this will measure the inherit
>variation of the variable, and not only the random error.
>
>So many of us uses a different star all together to estimate the
>uncertainty. I called it a check star but is should perhaps be called
>something else to avoid confusion. Since this star is subject to all
>the same processes that can produce uncertainty as the target star
>(except flat field issues) we use the std of this star as the
>measurement uncertainty for each data point, that is Std(K' - C) where
>K' is the instr.mag of this "check" star.
>
>Perhaps the concept of random and systematic error is less confusing
>than precision and accuracy :-) So this is one way to estimate random
>errors, but systematic errors from comp star catalogue values and
>transformations are not included. And you are right, I did not mean
>absolute magnitude but magnitudes on a standard system (I was thinking
>absolute as opposed to relative magnitude).
>
>Geir Klingenberg

-- 
Jeff Hopkins
HPO SOFT
http://www.hposoft.com/Astro/astro.html

*********************************************************
  Small minds speak about people * Average minds speak of events
************   Great minds speak of ideas!    ****************
*********************************************************
		     Hopkins Phoenix Observatory
  		       7812 West Clayton Drive
		   Phoenix, Arizona 85033-2439 U.S.A.
         			www.hposoft.com