[Placidus (Mike and Trish)]

Assuming floating point (not integer) arithmetic, there is no difference in signal to noise ratio between a sum combine and a mean combine.

Let's define signal to noise ratio of anything at all as coefficient of variation, i.e. value divided by standard deviation. Suppose you have 100 subs. The mean is the sum divided by 100. Dividing by 100 is just like changing centimeters to meters. It is a change of scale.

Suppose you have measured the length of a road in centmeters, and you are accurate to 10%. Re-expressing the length of the road in meters, or in kilometres, or in light years, won't increase the percentage accuracy or the fractional accuracy.

snr(sum) = sum / sd(sum)
snr(mean) = mean / sd(mean)
= (sum/100) / sd(sum/100)

what is sd(sum/100) ? Easy:

var(sum/100) = var(sum) / (100 * 100)
sd(sum/100) = sqrt[var(sum) / (100 * 100)]
= sd(sum) / 100

snr(mean) = sum/100 / sd(sum / 100)
= sum/100 / [ sd(sum) / 100 ]
= sum / sd(sum)
= snr(sum)

It's late and the wine was good and I've probably made 27 howling typos in the above but:

Suimmary: Dividing by a constant does not change the coefficient of variation. Changing from sum to mean is just a change of scale, like meters to centimeters. It does not change the accuracy of our photo. It does not change the signal to noise ratio.