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:

• The critical level LC, the signal level above which

an observed instrument response may be reliably

recognized as “detected.”

• The detection limit LD, the true net signal level that

may be expected a priori to lead to detection.

• The determination limit LQ, the signal level above

which a quantitative measurement can be performed

with a stated relative uncertainty.

Numerical values of these levels depend on four criteria, most importantly the standard deviation 0 of the

blank, or background. By choosing a probability 

(error of the first kind) for falsely deciding that the

Fig.1. “Ordered” detection limits—literature definitions. The detection limit for a specific radioactivity measurement process is plotted

in increasing order, according to commonly-used alternative definitions. LC, LD, and LQ are the critical level, detection level, and determination limit as derived in the text.

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signal is present when in fact it is not, the critical level

LC is calculable. Choosing a probability  (error of the

second kind) for deciding that the signal is absent when

it is in fact present permits the detection limit LD to be

calculated. Finally, specifying the maximum tolerable

statistical error in a quantitative measurement allows

the determination limit LQ to be computed. “The levels

LC, LD, and LQ are determined entirely by the errorstructure of the measurement process, the risks,  and

, and the maximum acceptable relative standard

deviation for quantitative analysis. LC is used to test an

experimental result, whereas LD and LQ refer to the

capabilities of [the] measurement process itself.”

Currie then gives recipes for calculating these

quantities, for the conventional assumptions of a normal

distribution; 5 % errors of the first and second kind; the

uncertainty of the blank independent of the signal level;

and quantitation at 10 % or better. His Table I has been

reprinted in many textbooks and operating manuals:

For radioactivity or a similar counting measurement,

where the data are digital and the distribution PoissonNormal, the equations are particularly simple; for

example, if the background is exactly zero with no

uncertainty, then LC = 0 counts, LD 2.71, and

LQ = 100. In agreement with experience, this means that

any observed count will be evidence of a non-zero

signal, and 100 counts gives a standard uncertainty of

100/(100) = 10 %. A more rigorous formulation for

LD, for extreme low-level counting, using the exact

Poisson distribution, was given by Currie in 1972. Here,

LD = 3.00 replaces the Poisson-Normal approximation

of 2.71 counts [2].

To make his 1968 paper still more concrete, three

specific illustrations of analytical procedures were

given, with worked-out equations for the three quantities: spectrophotometry, radioactivity, and a complex

case of activation analysis.

This seminal paper has been elaborated in many

contexts (e.g., [3]) and has led to an American Chemical

Society symposium on the topic [4]. Currie’s formulation was so convincing that it has been universally

incorporated in many rules of practice governing

measurement procedures, international standards [5],

regulations [6], and software. The culmination of

Currie’s early work was seen in the adoption of a

harmonized international position (ISO-IUPAC) on the

nomenclature, concepts, and formulation of detection,

decision, and determination limits [7]. The IUPAC position has been further embedded in the new edition of its

definitive guide for analytical chemistry [8]. Few scientific papers have been so definitive and decisive, or so

clearly set the standards of subsequent discourse. This

work is central to the NBS/NIST role in measurement

science.

Lloyd A. Currie attended the Massachusetts Institute

of Technology and then received his Ph.D. in 1955 at the

University of Chicago under Willard Libby. After

serving on the faculty at Pennsylvania State University,

he came to the National Bureau of Standards in 1962.

In addition to chemometrics, his specialty has been

atmospheric radioactivity, especially 37Ar and 14C.

His research group pioneered the application of microradiocarbon measurements for the discrimination of

anthropogenic and natural carbonaceous pollutants.

He has held visiting faculty appointments at the Universities of Bern and Gent, and was a Commerce Science

Fellow in the U.S. House of Representatives Science

Committee and the office of Congressman Mike

McCormack. He has served as a consultant or advisory

panel member for NASA, NSF, IAEA, IUPAC, and other

organizations. Currie is a Fellow of the American

Institute of Chemists, holds Department of Commerce

Gold and Silver Medals, and was named a NIST Fellow

in 1994.

Prepared by Richard M. Lindstrom.

Bibliography

[1] Lloyd A. Currie, Limits for Qualitative Detection and Quantitative Determination: Application to Radiochemistry, Anal. Chem.

40, 586-593 (1968).

[2] L. A. Currie, The Measurement of Environmental Levels of Rare

Gas Nuclides and the Treatment of Very Low-Level Counting

Data, IEEE Trans. Nucl. Sci. NS19 (1), 119-126 (1972).

[3] Lloyd A. Currie, The Many Dimensions of Detection in Chemical

Analysis—with Special Emphasis on the One-Dimensional

Calibration Curve, in Trace Residue Analysis: Chemometric

Estimations of Sampling, Amount, and Error, David A. Kurtz

(ed.), American Chemical Society, Washington, DC (1985),

pp. 49-81.

[4] Lloyd A. Currie, Detection: Overview of Historical, Societal,

and Technical Issues, in Detection in Analytical Chemistry (ACS

Symp. Ser. 361), L. A. Currie (ed.), American Chemical Society,

Washington, DC (1988) pp. 1-62.

Table I: “Working” Expressions for LC, LD, and LQ*

LC LD LQ

Paired observations 2.33 B 4.65 B 14.1 B

“Well-known” blank 1.64 B 3.29 B 10 B

*Assumptions:  =  = 0.05; kQ = 10;  = 0 = constant

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[5] Lloyd A. Currie, Nomenclature in Evaluation of Analytical

Methods Including Detection and Quantification Capabilities,

Pure Appl. Chem. 67, 1699-1723 (1995).

[6] Lloyd A. Currie, Lower Limit of Detection: Definition and

Elaboration of a Proposed Position for Radiological Effluent

and Environmental Measurements (Report NUREG/CR-4007),

U.S. Nuclear Regulatory Commission, Washington, DC

(1984).

[7] L. A. Currie, International Recommendations Offered on Analytical Detection and Quantification Concepts and Nomenclature,

Anal. Chim. Acta 391, 103-134 (1999).

[8] L. A. Currie, ch. 2 (Presentation of the Results of Chemical

Analysis) and ch. 18 (Quality Assurance of Analytical Processes),

in IUPAC Compendium of Analytical Nomenclature, Ja ́nos

Incze ́dy, Tama ́s Lengyel, and A. M. Ure, eds., Blackwell Science,

Oxford (1998).

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