= Limit of detection
A <limit of detection> describes how small an <analyte> amount or <concentration> an analytical procedure can distinguish from its background with a stated degree of certainty. It depends on the procedure, background variation and chosen decision rule. An <analytical blank> supplies measurements without the intended <analyte> contribution; its response need not be exactly zero.<Limit of detection in the IUPAC Gold Book>[L03540, definition and blank-mean/standard-deviation expression]{ref}
A simple model exposes the role of the decision rule. Suppose a single response satisfies $Y\sim N(\mu_B+ac,\sigma^2)$, with known blank mean $\mu_B$, positive response slope $a$, <analyte> <concentration> $c$ and constant known <standard deviation> $\sigma$. Choose the <detection decision threshold> $y_c=\mu_B+1.645\sigma$. Under the assumed <normal distribution>, a blank exceeds this threshold about5percent of the time. A sample whose mean merely equals $y_c$ exceeds it only half the time.
To obtain95percent probability of exceeding the same <detection decision threshold>, its mean must instead lie $1.645\sigma$ above it. The model therefore gives
$$
c_D\approx\frac{(1.645+1.645)\sigma}{a}=\frac{3.29\sigma}{a}.
$$
For $\sigma=2$ response units and $a=4$ response units per micromolar, $c_D\approx1.645\,\mathrm{\mu M}$. This is an original equal-variance, single-observation calculation, not a universal laboratory multiplier. Estimated blank uncertainty, unequal variance or a different error criterion changes the calculation. A detection claim also does not by itself establish a precise quantitative estimate of the <analyte> <concentration>.
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