Standard deviation of the blank

As discussed earlier, a concentration that would produce a signal of approximately 10-12 times the standard deviation of the blank (or in this case xeloq) is considered to be the limit of quantification. Therefore, if the LOQ was set at 10 times 5eloq, for 7 replicates (6 degrees of freedom) of the fortified control samples... 

Assuming that the standard deviation of the critical value is approximately equal to the standard deviation of the blank, scv Srl> it results for a = fi in... 

The DL and QL for chromatographic analytical methods can be defined in terms of the signal-to-noise ratio, with values of 2 1-3 1 defining the DL and a value of 10 1 defining the QL. Alternatively, in terms of the ratio of the standard deviation of the blank response, the residual standard deviation of the calibration line, or the standard deviation of intercept (s) and slope (5) can be used [40, 42], where ... 

The limit of detection (LoD) has already been mentioned in Section 4.3.1. This is the minimum concentration of analyte that can be detected with statistical confidence, based on the concept of an adequately low risk of failure to detect a determinand. Only one value is indicated in Figure 4.9 but there are many ways of estimating the value of the LoD and the choice depends on how well the level needs to be defined. It is determined by repeat analysis of a blank test portion or a test portion containing a very small amount of analyte. A measured signal of three times the standard deviation of the blank signal (3sbi) is unlikely to happen by chance and is commonly taken as an approximate estimation of the LoD. This approach is usually adequate if all of the analytical results are well above this value. The value of Sbi used should be the standard deviation of the results obtained from a large number of batches of blank or low-level spike solutions. In addition, the approximation only applies to results that are normally distributed and are quoted with a level of confidence of 95%. 

The determination of iron at trace levels can be accomplished by the spectrophotometric measurement of its complex with the reagent o-phenanthroline. The sensitivity of a particular method is 53 ppm per unit absorbance and the standard deviation of the blank estimated from 25 measurements is 0.002 of an absorbance unit. The practical detection limit is therefore 1.64aB or 0.0033 of an absorbance unit which corresponds to 0.17 ppm, and the theoretical detection limit is 3.28aB or 0.0066 of an absorbance unit which corresponds to 0.35 ppm. (The value of pB in this case is assumed to be zero.) Hence if a result is less than 0.17 ppm, the conclusion is that iron is not detected. If the value lies between 0.17 ppm and 0.35 ppm, the iron content should be reported as less than 0.35 ppm. ... 

It is an indicative valne and should not normally be nsed for decision-making pnrposes. It shonld be established nsing an appropriate measurement standard or sample and should not be determined by extrapolation. The LoQ is calculated as the analyte concentration corresponding to the sample blank value plus 10 standard deviations of the blank measurement. If measurements are made under repeatability conditions, a measure of the repeatability precision at this concentration is also obtained. 

Table V. Instrumental Detection Limits Based on Twice the Standard Deviation of the Blank...

A straightforward and widely accepted approach is to deem that an instrument response greater than the blank signal plus three times the standard deviation of the blank signal indicates the presence of the analyte. This is consistent with the approach shown in figure 8.4 if it is assumed that the standard deviation of a measurement result at the LOD is the same as that of a blank measurement. Suppose there is a linear calibration relation... 

If the measurement of LOD is not critical, an estimate can be made from the calibration parameters taking the intercept as the blank measurement and the standard error of the regression as the standard deviation of the blank. Equation (8.1) becomes... 

IUPAC the concentration giving a signal three times the standard deviation of the blank. 

From Eq. 2-96 optimization is thus possible by reducing the standard deviation of the blank value, by raising the number of blank measurements nb, and by using a method with a high sensitivity, a. ... 

Frequent use should be made of field and laboratory blanks these are essential for discovering the weak links in the sampling, handling, and analytical procedures. The blank results should also be used to correct measurements when necessary. The detection limits for the methods need to be quantified as 3 times the standard deviations of the blanks. The chemicals used may themselves be a source of contamination for some elements and have to be checked. 

The lowest concentration level at which a measurement is quantitatively meaningful is called the limit of quantitation (LOQ). The LOQ is most often defined as 10 times the signal/noise ratio. If the noise is approximated as the standard deviation of the blank, the LOQ is (10 x l)- Once again, when the recovery of the sample preparation step is factored in, the LOQ of the overall method increases by 1 /r. 

Limit of quantitation — (LOQ) The lowest amount of - analyte in a -> sample that can be quantitatively determined [i]. The LOQ is related to a signal value (j/q ) at which the -> analyte can surely be detected. It is defined by the following equation yq = pb + /cgoy, pb and standard deviation of the blank signal. The use of A q = 9 is recommended in order to have only a 0.135% of risk that a single signal measured in quantitative analysis is below the limit where it can be surely detected [ii]. 

Six 50-mg blank hair samples were extracted by SFE and the noise was integrated for the ion used for quantification (m/z = 355 for codeine, 369 for ethylmorphine, 383 for 6-MAM, and 397 for morphine) in a retention time window of tj + 0.5 min. The LOD and LOQ were determined (n = 6) using lUPAC methods. For each substance the standard deviation of the blank value (Sg) was determined. The mean area converted from the noise was calculated as concentration equivalent based on a calibration graph. The LOD is defined as 3Sg and the LOQ as lOSg. 

Figure 2.4(a) shows normal error curves (B and S) with true means / and ns for blank and sample measurements respectively. It is assumed that for measurements made close to the limit of detection, the standard deviations of the blank and sample are the same, i.e. aB = a% — a. 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 measure-mentswith true mean /tD will lie whilst point L on curve S represents a lower limit below which only 5% of sample measurements with true mean //s will lie. If /is now approaches /iB until points L on each curve coincide (figure... 

Fig. 3.10 Result of the limit of detection (LOD) determination for NS-TBA in binding buffer for the cognate target protein human a thrombin. The sensor was incubated with protein concentrations between 500 yM and 50 pM. The red line indicates the LOD (mean plus 3 standard deviations of the blank measurement) [49]...

The detection limit, defined as the element concentration corresponding to three times the standard deviation of the blank, is calculated to about 4 ng for antimony and tin and 2 ng for bismuth. When 400 m of air are fUtered and a 2 ml aliquot of the initial 50 ml sample solution is analyzed, practical detection limits are obtained of 0 25 ng m" for antimony and tin and 0.13 ng m" for bismuth. 

VL=Minimum detectable response=pbi + ( bi)j where pbi=mean of replicate analyses of a blank (a minimum of 20 is recommended), k=a numerical factor chosen according to the confidence level desired (a value of 3 is strongly recommended) and bi =the standard deviation of the blank responses. 5 is the sensitivity of the method. 

The standard deviation of the blank measurements is calculated (in units of response, not concentration). 

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