# Selectivity, Sensitivity, Signal to Noise, Detection Limit

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Selectivity, Sensitivity, Signal to Noise, Detection Limit

Selectivity This is an non-dimensional term, which can be expressed in %, that can quantify the selectivity of system for a specific target analyte. Let’s look at Example 1-2 in Skoog Holler Nieman (page 15).

Sensitivity... Ability of instrument to detect small changes in target analyte concentration. Two factors can be used to represent sensitivity. Slope of the calibration curve - recall this! Reproducibility (precision) of the measurement can affect the sensitivity. Sensitivity, precision and calibration curves are related. The calibration curves in the previous examples are optimal in that s or are negligible relative to the signal. Also, when two calibration curves have equal slopes, the one exhibiting better precision is more sensitive. High Low Response Conc.

...Sensitivity When the confidence interval around particular measurements is low, we find that sensitivity is compromised. Recall, sensitivity is the ability of the system to discriminate between analyte concentrations, so “noisy” measurements results in lower confidence about sensitivity. This example assumes a constant relative noise, say 5%. High Low Response Conc.

Quantitative Definition of Sensitivity
IUPAC defines sensitivity as calibration sensitivity This is the slope of the curve at the concentration of interest. Recall Response Factors, where RF=Response/Conc. Note, no consideration for precision with this approach. Signal Slope Signal for “Blank” Concentration Response Conc.

Analytical Sensitivity
This definition accounts for noise at a specific concentration. The slope can also be replaced with a response factor. Standard Deviation of the measurement Slope Analytical Sensitivity Consider the use of an analytical balance. ASTM provides guidelines on the acceptable threshold of noise on the sensitivity of the balance (USP reference). Amplification of the signal won’t be the answer since this will also increase the Ss. A disadvantage is that  is concentration depend.

Signal to Noise Ratio (S/N) (Chpt. 5, Skoog Holler Nieman)
This definition accounts for noise at a specific concentration. The slope can also be replaced with a response factor. Standard Deviation of the measurement Mean Response Signal to Noise Ratio This definition should look familiar... What is NOISE… recall previous discussions. Simply, it is unwanted signal that can affect the proper detection and quantification of a desired signal. The S/N ratio has a direct impact on LOD.

Noise and Detection Limit...
Noise has a direct effect on detection limit. The detection limit represents that concentration of signal which is no longer reproducibly or reliably discernable from noise, at which point no accurate statement about analyte concentration can be made. Summary: we can see a signal due to the analyte but can’t exactly quantify the analyte concentration. Estimated Analyte Concentration Using Test Method Let’s review: LOQ (blank + 10  blank) LOD or MDL Increasing Confidence Not Detectable

...Noise and Detection Limit...
ACS - basic definition of detection limit (see equation below). The ACS approach is generally accepted; however, it has numerous limitations which we will explore. Note that k is usually taken as 3. Standard Deviation for “Blank” Mean blank signal Minimum Distinguishable Analytical Signal Slope Detection Limit

...Noise and Detection Limit...
Reducing noise or improving the signal will give better detection limits. For example, signal averaging (see below) appears to pull the signal out of the noise. What is happening here is due to the fact that “Noise is Random”. Therefore, with enough acquired data, the noise will eventually cancel itself out. Consider the concept of constructive and destructive waves. Below is an example of the effect of S/N ratio on the NMR spectrum of progesterone.

The Light Bulb... Consider a 10 W light bulb, violet light. In absolute darkness, that bulb, when turned on, would be quite simple to detect. In fact, depending on the detector, say your eye, you should even be able to tell the difference between 5 W, 10W and 15 W light bulbs. What if the background was contaminated, say with light from a 1 W yellow light bulb. Now, what if the background was contaminated with light from fifty 1 W yellow light bulbs. Would you still be able to see the 10 W violet light bulb with that background? O R V B G Y Yellow Filter

More on S/N & Detection Limits...
It must be appreciated that detection limits are not “fixed” values, and will change with time, analyst, equipment, etc. Detection limits require that we can distinguish between a background or blank signal and a signal from a target analyte. A quantitative determination is typically taken as a system with less than 10% RSD, less for more serious applications such as pharmaceutical. The ACS has defined three important levels for measurement of data LOD (blank signal+3blank) RDL (blank signal+6blank) LOQ (blank signal+10blank)

... More on S/N & Detection Limits
It must be appreciated that detection limits are not “fixed” values, and will change with time, analyst, equipment, etc. Normally distributed data will allow you to better estimate the contribution of noise to your desired signal.

Type I and Type II Decision Errors
The null hypothesis: No difference between the blank and sample (non-detect) (µA=µB). The alternative hypothesis: The sample response is greater than the blank (detection) (µA>µB). Type I Decision Error: Rejecting the null hypothesis when it is true (false positive) () Type II Decision Error: Accepting the hypothesis when it is false (false negative) () So, two errors are possible: False Positives and False Negatives depending on the hypothesis.

Decision Errors

Detection Limits - ACS vs. U.S.EPA

Detection Limits - U.S.EPA

S/N - Root Mean Square