deviations of the blank and sample are the same, i.e. σB = σS = σ. In most cases, a 95% confidence level
is a realistic basis for deciding if a given response arises from the presence of the analyte or not, i.e.
there is a 5% risk in reporting the analyte 'detected' when it is not present and vice versa. Thus, point L
on curve B represents an upper limit above which only 5% of blank measurements with true mean μB
will lie, whilst point L on curve S represents a lower limit below which only 5% of sample
measurements with true mean μS will lie. If μS now approaches μB until points L on each curve coincide
(Figure 2.4(b)), the point of coincidence represents the practical detection limit for a single
measurement, i.e. if a measurement falls at or below L, it has a 95% probability of arising from
background sources or random noise only, whilst if it falls above L it has a 95% probability of arising
from the presence of the analyte. Furthermore, it follows that μS must now represent the theoretical
detection limit because a true mean lying below μS would have a normal distribution with more than 5%
of values below L. Because the chances of making an incorrect decision were chosen to be equal in this
case (5% probability), then μS is given by
Individual practical results falling between L and μS must be regarded as 'detected' but should be
reported as 'less than μS'.
The value of L and hence of μS is related to σ and is given by
Figure 2.4
Normal error curves for blank B and sample S measurements.