page_title: Detection limit
hierarchical_section_title: Detection limit
caption_attribution_description: Illustration of the concept of detection limit and quantitation limit by showing the theoretical normal distributions associated with blank, detection limit, and quantification limit level samples.
context_page_description: 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(x) = a + b(x)" where "f(x)" 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(x) 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.
context_section_description: In analytical chemistry, the detection limit, lower limit of detection, or LOD (limit of detection), often mistakenly confused with the analytical sensitivity, is the lowest quantity of a substance that can be distinguished from the absence of that substance (a blank value) with a stated confidence level (generally 99%).  The detection limit is estimated from the mean of the blank, the standard deviation of the blank, the slope (analytical sensitivity) of the calibration plot and a defined confidence factor (e.g. 3.2 being the most accepted value for this arbitrary value).  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(x) = a + b(x)" where "f(x)" corresponds to the signal measured (e.g. voltage, luminescence, energy, etc.), "a" the value in which the equation cuts the ordinates axis, "b" the sensitivity of the system (the slope of the plot or the function interacting with the measurable variable) and "x" the value which is measured (e.g. temperature, concentration, pH, etc.), the LOD is calculated as the "x" value in which f(x) equals to the average value of blanks "y" plus "t" times its standard deviation "s" (or, if zero, the standard deviation corresponding to the lowest value measured) where "t" is the chosen confidence value (e.g. for a confidence of 95% it can be considered t = 3.2, determined from the limit of blank). Thus, LOD = (f(x)-a)/b = (y + 3.2s - a)/b.
  There are a number of concepts derived from the detection limit that are commonly used.  These include the instrument detection limit (IDL), the method detection limit (MDL), the practical quantification limit (PQL), and the limit of quantification (LOQ).  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 (LOD), and the limit of quantification (LOQ) 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 (probability of false positive) is small (1%).  However, the beta error (probability of a false negative) is 50% for a sample that has a concentration at the LOD (red line).  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 (blue line), there is minimal chance of a false negative.
caption: Illustration of the concept of detection limit and quantitation limit by showing the theoretical normal distributions associated with blank, detection limit, and quantification limit level samples.
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