In analytical chemistry, the detection limit, lower limit of detection, or LOD, often mistakenly confused with the analytical sensitivity, is the lowest quantity of a substance that can be distinguished from the absence of that substance with a stated confidence level. The detection limit is estimated from the mean of the blank, the standard deviation of the blank, the slope of the calibration plot and a defined confidence factor. Another consideration that affects the detection limit is the accuracy of the model used to predict concentration from the raw analytical signal. As a typical example, from a calibration plot following a model equation "f = a + b" where "f" corresponds to the signal measured, "a" the value in which the equation cuts the ordinates axis, "b" the sensitivity of the system and "x" the value which is measured, the LOD is calculated as the "x" value in which f equals to the average value of blanks "y" plus "t" times its standard deviation "s" where "t" is the chosen confidence value. Thus, LOD = /b = /b. There are a number of concepts derived from the detection limit that are commonly used. These include the instrument detection limit, the method detection limit, the practical quantification limit, and the limit of quantification. Even when the same terminology is used, there can be differences in the LOD according to nuances of what definition is used and what type of noise contributes to the measurement and calibration. The figure below illustrates the relationship between the blank, the limit of detection, and the limit of quantification by showing the probability density function for normally distributed measurements at the blank, at the LOD defined as 3 * standard deviation of the blank, and at the LOQ defined as 10 * standard deviation of the blank. For a signal at the LOD, the alpha error is small. However, the beta error is 50% for a sample that has a concentration at the LOD. This means a sample could contain an impurity at the LOD, but there is a 50% chance that a measurement would give a result less than the LOD. At the LOQ, there is minimal chance of a false negative.
Instrument detection limit
Most analytical instruments produce a signal even when a blank is analyzed. This signal is referred to as the noise level. The IDL is the analyte concentration that is required to produce a signal greater than three times the standard deviation of the noise level. This may be practically measured by analyzing 8 or more standards at the estimated IDL then calculating the standard deviation from the measured concentrations of those standards. The detection limit is the smallest concentration or absolute amount of analyte that has a signal significantly larger than the signal arising from a reagent blank. Mathematically, the analyte’s signal at the detection limit is given by: . where Sreag is the signal for a reagent blank, is the known standard deviation for the reagent blank’s signal. Other approaches for defining the detection limit have also been developed. In atomic absorption spectrometry usually the detection limit is determined for a certain element by analyzing a diluted solution of this element and recording the corresponding absorbances. The experiment is repeated for 10 times. The 3σ of the recorded absorbance signal can be considered as the detection limit for the specific element under the experimental conditions used – wavelength, type of flame, instrument.
Method detection limit
Oftentimes there is more to the analytical method than just performing a reaction or submitting it to direct analysis. For example, it might be necessary to heat a sample that is to be analyzed for a particular metal with the addition of acid first. The sample may also be diluted or concentrated prior to analysis on an instrument. Additional steps in an analysis add additional opportunities for error. Since detection limits are defined in terms of error, this will naturally increase the measured detection limit. This detection limit is called the MDL. The practical method for determining the MDL is to analyze 7 samples of concentration near the expected limit of detection. The standard deviation is then determined. The one-sided t-distribution is determined and multiplied versus the determined standard deviation. For seven samples the t value for a 99% confidence level is 3.14. Rather than performing the complete analysis of seven identical samples, if the Instrument Detection Limit is known, the MDL may be estimated by multiplying the Instrument Detection Limit or Lower Level of Detection by the dilution prior to analyzing the sample solution on the instrument. This estimation, however, ignores any uncertainty that arises from performing the sample preparation and will therefore probably underestimate the true MDL.
Limit of quantification
The LOQ is the limit at which the difference between two distinct values can be reasonably discerned. The LOQ may be drastically different between laboratories so another detection limit is commonly used that is referred to as the Practical Quantification Limit.
