Averaging versus Stacking
OK Forum Friends, I am still a bit new at this, so be kind. :)
From what I can understand, AAVSO recommends more than one image of a field. I take four as four as the minimum needed to get a standard deviation of the average magnitude of four estimates. So, when I have a target with SNR > 100 I compute the magnitude for the target in each image and then average the results and obtain an appropriate uncertainty with N=4. I do not stack. I figure that the uncertainties associated with each image estimate are not relevent and it is the uncertainty of the average over four estimates that is relevent. So each image estimate might have a rather large standad deviation due to differences in color in the ensemble, but the mean and standard deviation of the four images is more reflective of the actual uncertainty.
Example: NSVS J0426046+163402 (SNR = 98, pretend it does not vary over short time periods)
Range = 12.765-12.787 (VMag)
Average = 12.77V; StDev target = 0.013
Now--- if you take any one image, the Std of the variable and the ensemble is somewhere in the range of 0.04 - 0.08 (VPHOT error). This can be improved for a single image by eliminating comp stars. However, I thought the idea of multiple images and ensembles was not to eliminate comps but let the "law of averages" work over several images. If you look at any ensemble it is quite possible to eliminate comps to improve your uncertainty, but I don't think it really helps compared to averaging over images. For example, the best I could do by eliminating all but 2comps for a single image is VPHOT error = 0.011. But if I am concered about a 0.002 difference, I can simply add another image or integrate longer for better SNR. (For example, if I simply add a fifth image that is around the mean I get a StDev of the variable of 0.011.) Further, even if I eliminate comps to "beat down" the uncertainty of single images, neither the average or the uncertainty over the four images necessarily improves, in fact, it can be worse.
For example, I eliminated two comps bringing my individual image uncertainty down about 0.02/image. But my average did not change (12.77V) and uncertainty over the four images increased to 0.015. Naturally, I have no degrees of freedom to argue this point as this is a single example. But I am wondering if I am on the right track.
BTW, if I stack I get a full ensemble of comp stars and a variable uncertainty of 0.020. I can improve that by eliminating comp stars, but is this good practice given that I have adaquate SNR in each image and thus can average?