Effect of signal-to-noise ratio on sampling variability

As signal-to-noise ratio increases, the amount of variability decreases for the same number of samples. This indicates that one way to reduce variability is to test with a higher signal-to-noise ratio. This may of course be impractical. Many psychophysical experiments are run that use levels of signal-to-noise ratio as an independent variable.

The other obvious question is what effect do different distributions have on the standard deviation of the area?