A method’s detection limit is the smallest amount or concentration of analyte that can be detected with statistical confidence.

Detection Limits

A method’s **detection limit
**is the smallest amount or concentration of analyte that can be detected
with statistical confidence. The International Union
of Pure and Applied
Chemistry (IUPAC) defines
the detection limit
as the smallest concen-
tration or absolute amount of analyte that has a signal significantly larger than the signal arising from a reagent blank.
Mathematically, the analyte’s signal at the
detec- tion limit, (*S*_{A})_{DL}, is

4.25

where
*S*_{reag} is the signal for a reagent blank, σ_{reag} is the known standard devia- tion for the reagent
blank’s signal, and *z *is a factor accounting
for the desired
confidence level. The concentration, (*C*_{A})_{DL}, or absolute amount of analyte,
(*n*_{A})_{DL}, at the detection limit can be determined from the signal at the detection limit.

The value for *z *depends on the desired
significance level for reporting the detection
limit. Typically, *z *is
set to 3, which, from
Appendix 1A, corresponds to a signifi- cance level of α = 0.00135.
Consequently, only 0.135%
of measurements made on
the blank will yield signals
that fall outside
this range (Figure
4.12a). When σ_{reag} is unknown, the term
*z*σ_{reag} may
be replaced with
*ts*_{reag}, where
*t
*is the appropriate value from a *t*-table for
a one-tailed analysis.

In analyzing a sample to determine whether
an analyte is present, the
signal for the sample
is compared with the signal
for the blank.
The null hypothesis is that the sample
does not contain
any analyte, in which case
(*S*_{A})_{DL} and *S*_{reag} are identical. The alternative hypothesis is that the analyte
is present, and (*S*_{A})_{DL} is greater than *S*_{reag}. If (*S*_{A})_{DL} exceeds
*S*_{reag} by *z*σ(or
*ts*), then the null hypothesis is rejected and there is evidence for the analyte’s presence in the sample. The proba-
bility that the null hypothesis will be falsely
rejected, a type
1 error, is the same
as the significance level. Selecting
*z
*to be 3 minimizes the probability of a type 1
error to 0.135%.

Significance tests, however,
also are subject
to type 2 errors in which the null
hypothesis is falsely retained. Consider,
for example, the situation shown in Figure 4.12b, where *S*_{A} is exactly equal
to (S_{A})_{DL.} In this case the probability of a type 2
error is 50% since half of the signals arising
from the sample’s
population fall below the
detection limit. Thus,
there is only
a 50:50 probability that an analyte
at the IUPAC detection
limit will be detected. As defined, the IUPAC definition for the detection limit only indicates
the smallest signal for which we can say, at a significance level of α, that an analyte is present in the sample.
Failing to detect
the analyte, however,
does not imply
that it is not present.

An alternative expression for the detection limit, which minimizes both type 1 and
type 2 errors,
is the **limit of identification, **(*S*_{A})_{LOI}, which
is defined as

As shown in Figure 4.12c,
the limit of identification is selected such that there
is an equal probability of type 1 and type 2 errors.
The American Chemical
Society’s Committee on Environmental Analytical Chemistry recommends the **limit of quantitation, **(*S*_{A})_{LOQ}, which
is defined as

Other approaches
for defining the detection limit have also been developed.

The detection limit
is often represented, particularly when used
in debates over public policy issues, as a distinct
line separating analytes
that can be detected from that cannot be detected.17 This use of a detection limit is incorrect. Defining the detection limit
in terms of statistical confidence levels implies that there may be
a gray area where the analyte is sometimes detected
and sometimes not detected.
This is shown in Figure
4.13 where the upper and lower confidence limits are de- fined by the acceptable probabilities
for type 1 and type 2 errors. Analytes produc- ing signals greater than that defined
by the upper confidence limit
are always de- tected, and analytes giving
signals smaller than
the lower confidence limit are never detected. Signals falling between
the upper and lower confidence limits, however, are ambiguous because they
could belong to populations representing either the reagent blank
or the analyte. Figure 4.12c represents the smallest value
of *S*_{A} for which no such ambiguity exists.

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Modern Analytical Chemistry: Evaluating Analytical Data : Detection Limits |

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