Analytical Chem istry - DePauw University

Chapter 4 Evaluating Analytical Data119S mb(SA ) DLof analytes that concentrations that cannot be detected. This use of a detectionlimit is incorrect. 13 As suggested by Figure 4.16, for concentrationsof analyte near the detection limit there is a high probability of failing todetect the analyte.An alternative expression for the detection limit, the limit of identification,minimizes both type 1 and type 2 errors. 14 The analyte’s signalat the limit of identification, (S A ) LOI , includes an additional term, zs A , toaccount for the distribution of the analyte’s signal.( S ) = ( S ) + zσ = S + zσ + zσA LOI A DL A mb mb AAs shown in Figure 4.17, the limit of identification provides an equal probabilityfor type 1 and type 2 errors at the detection limit. When the analyte’sconcentration is at its limit of identification, there is only a 0.135%probability that its signal will be indistinguishable from that of the methodblank.The ability to detect the analyte with confidence is not the same asthe ability to report with confidence its concentration, or to distinguishbetween its concentration in two samples. For this reason the AmericanChemical Society’s Committee on Environmental Analytical Chemistryrecommends the limit of quantitation, (S A ) LOQ . 15( S )(S A) LOI= S +10σA LOQ mb mbFigure 4.17 Normal distribution curves for a method blank and for asample at the limit of identification: S mb = 0; s mb = 1; s A = 0.8; and(S A ) LOI = 0 + 3 × 1 + 3 × 0.8 = 5.4. The inset shows that the probabilityof a type 1 error (0.135%) is the same as the probability of atype 2 error (0.135%).13 Rogers, L. B. J. Chem. Educ. 1986, 63, 3–6.14 Long, G. L.; Winefordner, J. D. Anal. Chem. 1983, 55, 712A–724A.15 “Guidelines for Data Acquisition and Data Quality Evaluation in Environmental Chemistry,”Anal. Chem. 1980, 52, 2242–2249.