How exactly is analog Signal to Noise Ration (SNR) defined?
It is not clear from your question if you are referring to ADC measurements using volts (typical would be counts) or if you are referring to the ADC input. However your question on SNR can apply to either case. Your reference to a "threshold" is unclear.

The signal to noise ratio is typically referred to the signal power, which occupies a bandwidth, as a ratio to the noise power over that same bandwidth.  Any other noise we have the opportunity to filter out in our subsequent processing. 

Also, the noise power with reference to a voltage reading would proportional to the square of the rms voltage (1 sigma) not the peak-peak (which could be 6 sigma or more).

Further, this rms voltage would be representative of the (square root of the) power across the entire measurement bandwidth (in terms of an analog measurement), or the digital Nyquist bandwidth in terms of an ADC output (and again here I would use rms counts, where counts are increments of the lsb of the ADC).  

So to compute SNR, if you are using rms quantities, it would be 20 Log the ratio of the rms signal to the rms noise in band. If you are using rms squared (power or variance) quantities, it would be 10 log the ratio of the variance of the signal to the variance of the noise is band (the portion of the noise that occupies the same bandwidth of the signal).