You are not averaging, you are adding, to get the lower noise you have to divide by the number of pixels you have added together, in this case four. Take any one pixel of information and it has to fit in the bit depth, for 14 bit that is 16,385, if you add four together you can't have a number higher than 16,385, so you have to divide by that same number to keep your range constant.

So take your last block of four, if noise becomes visible, your noise floor, at 3 (for example) you have two noisy pixels px-ID-14 and px-ID-15, if you add the four together you get 8, then divide by four you get 2 per pixel, which you can't see. Voila, two pixels that had visible noise don't now have visible noise, but you have lost the ability to differentiate detail in those four pixels so you now have one noiseless pixel instead of two of four noisy ones.

To be sure, your DR has not increased in that you don't have a wider range, you can't see below your noise floor and the bit depth has not increased because add four and divide by four is a zero sum when confined to whole numbers. You have lowered the noise levels by averaging/downsampling though.

Hi PBD, thanks for the reply.

I don't know if I'm just retarded, but I still don't get it. I included a division process in the averaging my original spreadsheet here is an update I just changed the layout to put the averages in at the bottom of the table (see attached)

Is my concept of average image noise flawed (i.e. Average image noise = sum of pixel noise divided by number of pixels)

Yes, you don't average the first group.

So take your first four pixels, say the noise floor is 4, ID-2 and ID-4 are both noisy pixels, at 100% view those pixels are garbage. Add the four together and divide by four and the resulting value is 3, so that block of four pixels, that is now one number is no longer noisy, at 100% view that down sampled one pixel (the four have become one) is not noisy but the picture is 1/4 the size it was.

This is how multiple exposures reduces noise on a same size basis, take various exposures of the same thing, add them together and divide by the number of exposures and you get less noise and retain the number of pixels. Basic astrphotography.

Is my concept of average image noise flawed (i.e. Average image noise = sum of pixel noise divided by number of pixels)

Yes this concept is wrong. Remember, you are not adding up all the values and dividing by the total number of pixels, you are only adding the down sampled pixels together and dividing by that number of pixels to get a new averaged pixel value. Then the number of actual pixels that fall into the range of noise is lower, but so is detail!

P.S. You can't have decimal places in your averages (you'd need more bit depth), so in the adjusted table below the .5 and above would be rounded up, .49 and lower would be rounded down. So you'd actually have 6 - 3 - 1.