The limits of detection (LOD), determination, and quantification (LOQ) are terms commonly used in the field of analytical chemistry and define specific signal values. However, what do they actually mean and why are they defined the way they are?
| Definition | Colloquial | |
| Limit of detection | The lowest signal that might be confused with baseline noise in only 0.3% of the observations. | “I know there is something!” |
| Limit of determination | The lowest signal that can be distinguished from the baseline noise with higher statistical certainty. | “I know for sure there is something!” |
| Limit of quantification | The lowest signal that can be distinguished from the baseline noise with statistical certainty and assigned numeric value that corresponds to the analyte’s concentration. | “I know for sure there is something and I can tell you how much it is.” |
Calculation
The limits of detection, determination, and quantification can be calculated using the blank method or the calibration method.
Blank method
The blank method is based on the assumption that the obtained response when measuring a blank is solely dependent on the instrument error, which is the random fluctuation of the baseline signal. Hence, the analyte’s signal must be significantly different from the baseline signal to be considered as “detected”. Each baseline signal we measure lies within a normal distribution. As we might remember from our basics of statistics lectures from back in the days, around 95% of normally distributed data lies within an interval of +/- three times the standard deviation of the data. If we thus want to be sure that a signal does, with high probability, not originate from random baseline noise, we will only accept signals that are at least three times higher than the standard deviation of the baseline signal. This is our limit of detection.
\text{LOD} = 3 \cdot \text{sd}If we want to be very sure that the signal we measure is actually originating from the analyte, then we would choose the limit of determination instead, which is twice the limit of detection.
\text{LODeterm} = 2 \cdot \text{LOD} = 6 \cdot \text{sd}Choosing the limit of determination over the limit of detection gives additional statistical security, but may lead to false-negative results (= below LODeterm).
The limit of quantification, meanwhile, is defined as the threshold value at which it is possible to induce a quantitative outcome with statistical security. It is calculated by multiplying the standard deviation by ten.
\text{LOQ} = 10 \cdot \text{sd}Calibration method
The calibration method can be used to determine the limit of detection from the calibration curve. In some cases, this might be favourable, for instance if you observe non-linearity of your responses at the lower end of your working range.
A simplified but generally accepted way to calculate the LOD is by multiplying a correction factor (usually 3.3) with the standard deviation of the regression residuals of the calibration curve and divide the product by the slope of the calibration curve.
\text{LOD}=\frac{k \cdot s_{y}}{m}The LODeterm and LOQ can eventually be obtained analogous to the blank method.