Chromatography Forum

Hi All

I was curious to ask something. I notice that the USP defines signal-to-noise ratio as 2 x Signal/Noise (this is in Section <621>).

It seems to me that most textbooks - and also common logic - would define Signal to Noise ratio simply as Signal/Noise.

Any insight or thoughts as to why they defined it this way? Why the factor of two?

Thanks in Advance

I always had a problem with how archaic the USP definitions of S/N ratio, LOD, and LOQ are, especially in the advent of HRMS and how low our noise values actually got. True LOD/LOQ should be calculated with a detection limit study (like the EPA requires) and not just be 3:1 and 10:1 of signal to S/N as currently defined. </rant>

As for your question, I suspect it has to do with trying to make up for the overlap in signal area in the noise regions. See Figure 5 in this document https://www.bioglobax.com/wp-content/up ... graphy.pdf

But I agree USP needs to completely overhaul that measurement, or at least make separate definitions depending on what detector is being used.

You're not alone with your question.

Years ago, even John Dolan questioned where the factor 2 was coming from

https://www.chromforum.org/viewtopic.ph ... ise+ep+usp

From a statistical point of view, the noise is just like a Gaussian distribution of random-signals, centered around 0 (Gaussian apex).
Then the width would reflect +/- 1 standard deviation (=2s)
A signal is then regarded as real (not noise), with a certainity of >99%, if it is more than 3s away from the Gaussian average.
So it is a matter of one sided vs two sided distribution or more or less certainity.

(That's how I understand the situation)

USP defines signal-to-noise ratio as 2 x Signal/Noise

It is not 2 x Signal/Noise. Is is Signal/Noise, wherein the Signal is H, and the Noise is h/2, i.e. S/N = H/(h/2). This definition of noise is just one of the several possible definitions.

The choice of the definitions for noise and for S/N, as well as the choice of the limits for S/N (S/N > 2, S/N > 3, S/N > 10, etc), are just a matter of agreement between the users of these definitions and limits for some purposes. The values of S/N (with any definitions) are correlated with LOQ and LOD. However, the actual LOD is a matter of confident discrimination of the useful signal from the useless noise for qualitative analysis. The required level of confidence may vary in various applications.

The actual LOQ is a matter of precision of the signal (the signal here is usually the peak area) at low amounts of the analyte. The minimum required precision may vary in various applications.

The limit S/N = 10 (with any definition of noise) is in no way a universal indicator that the signal and/or the analyte quantity correspond to the real LOQ that complies with the requirements to the method precision.