Limits for Qualitative Detection and Quantitative Determination

A visiting professor at NIST once pointed out that our measurement professionals are given a difficult task by some of our customers. In a (macroscopically) continuum universe, we are asked to perform measurements with tools and techniques of finite precision and in the end to produce digital answers, preferably binary: yes or no, safe or unsafe, above or below the regulatory limit. A common triple question arises in the measurement of environmental radioactivity, atmospheric ozone, gold in rock, or the efficacy of a flu treatment: Is the signal there? What is the chance that we will detect it? How big is it? Until Lloyd Currie’s paper Limits for Qualitative Detection and Quantitative Determination: Application to Radiochemistry [1] was published, there was enough inconsistency in the definition of “detection limit” to conceal a great deal of disagreement. In just over seven pages, this tightly written communication established a high level of uniformity in answering these questions. The paper contains fundamental information that has made it influential far beyond its size, and it is rich enough to be discussed actively in e-mail newsgroups over 30 years later. This is surely one of the most often cited publications in analytical chemistry. The Science Citation Index lists 1280 published references to this paper—so far. Currie asks and answers a disarmingly simple question: What do we mean by the detection limit of a measurement process? He found that the literature “revealed a plethora of mathematical expressions and widely-ranging terminology.” The same terms have been used to denote both the amount that can be detected and the amount that can be measured, which are very different quantities. Statistical justification for some common recipes has been absent or incorrect. To show graphically how serious the problem was (and is), he used literature definitions to compare detection limits, defined by eight common recipes, or rules of thumb, for a simple measurement: counting a radioactive source for 10 minutes with a detector that is 10 % efficient and has a background of 20 counts per minute. Currie then arranged the values of the detection limit in serial order, and found that the range of these definitions spans a factor of nearly 1000. His Figure 1, reproduced here, clearly showed the need for a consistent, statistically and physically defensible, definition of this common term. Currie then defined measures of detectability, firmly based on the statistical theory of hypothesis testing. He began by defining the concepts of qualitative and quantitative analysis limits. Three limiting levels were defined: