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A detection decision threshold is a cutoff applied to an observed analytical response to decide whether there is evidence for an analyte contribution beyond background. A decision above the cutoff can be wrong even for an analytical blank: this is a type I error. Missing a genuine contribution is a type II error. The chosen rule and the measurement procedure determine those error probabilities.^[ref]

For an original one-sided example, suppose blank responses have a known normal distribution $Y\sim N(100,5^2)$. Set $y_c=100+1.645(5)\approx 108.225$. Declaring detection when $Y>y_c$ gives about a5percent type I error probability. A real sample whose mean is exactly $108.225$ has only a50percent chance of crossing that same detection decision threshold.

Under the additional assumption of unchanged standard deviation, a mean near $116.45$ gives about95percent probability of crossing it: the mean lies another $1.645(5)$ units above $y_c$. Thus an observed-response cutoff and a limit of detection giving a specified detection probability answer different questions. These numbers are a known-variance teaching model, not a universal laboratory convention. Estimating the background, changing the error criterion or allowing signal-dependent variance changes the calculation. The threshold must be tied to the complete procedure whose detection performance is claimed.^[ref]

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.^[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 givesFor $\sigma =2$ response units and $a=4$ response units per micromolar, $c_D\approx 1.645\mu \mathrm{M}$. 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.

Lloyd A. Currie prepared the 1995 IUPAC recommendations on evaluating analytical methods, including detection and quantification capabilities. A central contribution was to separate an observed-result decision from the capability of a measurement process. A detection decision threshold controls the chance of a false positive, while a limit of detection also depends on the chance of missing a real signal.^[ref]

An original idealized example makes the distinction visible. Suppose the blank-corrected measurement has a normal distribution with standard deviation one. A threshold near $1.645$ gives a 5% type I error under a zero-mean blank model. A true mean near $3.29$ places that same threshold about $1.645$ standard deviations below the mean, giving about 95% detection probability, or 5% type II error.

The two signal levels answer different questions: whether one observed result crosses a decision boundary, and how strong a true signal must be for reliable detection under the assumed process. These numbers belong to the stated model; they are not universal detection limits for instruments.