= Detection decision threshold
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.<Nomenclature in evaluation of analytical methods including detection and quantification capabilities by Lloyd A. Currie>[§§3.7.2–3.7.3, page1709]{ref}
For an original one-sided example, suppose blank responses have a known <normal distribution> $Y\sim N(100,5^2)$. Set $y_c=100+1.645(5)\approx108.225$. 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.<Nomenclature in evaluation of analytical methods including detection and quantification capabilities by Lloyd A. Currie>[§3.7.2, process specification; §3.7.3, separate error probabilities]{ref}
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