Limits, of decision

A sample whose analyte concentration is below the limit of decision of the analytical procedure being used. 

The analytical value (e.g. the concentration) that corresponds to the critical value. The limit of decision is of minor importance in analytical chemistry because the detection at this level of concentration succeeds only in 50% of all cases. 

Several analytical papers deal with the construction of such intervals (see, e.g., [EBEL, 1983 EBEL et al., 1983 1989]. Details of exact predictions, especially for limits of decision, detection, and determination (see Section 2.4.12) are considered by LUTHARDT etal. [1987]. 

If the signal of any test sample is above this critical value, then, with a certain error risk of, say, a = 0.05, one can decide that the signal comes from an analyte present in the sample. According to this qualitative decision the corresponding critical concentration xcrit xdecision, the limit of decision, is easily calculated by combination of the above given calibration equation, Eq. 2-92, for y=ycrit and Eq. 2-95 assuming Hasty blank = ad-... 

The numerical value of the limit of decision can also be reduced by taking into account the future analytical effort involved in na. If for the analyzing step the same standard deviation as for the blank determinations can be ensured, the limit of decision is ... 

Here one recognizes another way of optimizing, namely to set up a calibration experiment with xc close to the limit of decision. Consequently is has been recommended that the highest concentration should be below 10 xdecision. 

Historically, the simple so-called fax -criteria are based on the standard deviation ( cr ) of blank measurements. The limit of decision ( Nachweisgrenze ) has been defined at k=3, the limit of detection ( Erfassungsgrenze ) at k = 6, and, among other possibilities,... 

Sometimes the single parent needs to clarify the limits of decision making to which the only child is entitled. "Just because I want you to understand and help me think about where our money goes, that doesn t mean you get to choose the way we spend. It s my job to determine what we can afford." The only child needs to understand that input doesn t guarantee outcome, that influence doesn t mean control, that responsibility doesn t mean authority, that adults are not bound by many of the rules a child must live by, and that being a "partner" in the family doesn t entitle him or her to an equal say. An only child of a single parent can presume more power of responsibility than is appropriate. 

Note 7. Method-specific mechanistic understanding is, in the last analysis, the only route to reliable measurements, reliable detection limits, and meaningful societal decisions involving science related public policy. The need for understanding on the mechanistic level becomes even clearer when one considers the inherent limitations of decisions and policies based solely on the empirical record, such as certain aspects of epidemiology. Sampling statistics and control of the system under investigation empirically, constitute severe limitations -- ones that can be... 

In many cases, maximrun residue limits (MRLs) exist for veterinary drugs and the analytical methods must be capable of measming below such MRLs. Since MRLs vary considerably, the sensitivity requirements of the various methods also vary widely. Typically, MRLs for veterinary drug residues vary from Imgkg (ppm) to Ipgkg (ppb) (Table 1) or, in the case of banned substances, to no detectable residue . Where no detectable residue is specified, it is common to declare an action limit or a limit of decision for use by regulatory agencies this is not strictly scientifically based and takes into account other aspects such as the sensitivity of a suitable confirmatory technique and policy requirements. 

Figure 5.7 Definitions of the limit of decision and the limit of detection.

Figure 5. Limit of decision rj and of detection Xd A) Calibration function in presence of a blank B) Probabilities for the detection of an impurity at limit of decision (upper curve) and at limit of detection (lower curve)...

Therefore the limit of decision never can be used as guarantee of purity. A sufficiently high reliability for such a guarantee is given for the signal value... 

A fully defined trace-analytical procedure is characterized by the concentration range, as well as the calibration function, the precision and accuracy, and the limits of decision, detection, and possibly quantitation. The use of the three last-mentioned terms in the literature unfortunately is not uniform and requires international standardization. 

The limit of decision is an important criterion in the optimization of a trace-analytical procedure and the comparison of methods. It depends greatly on possible errors in individual steps. It can be determined in many different ways, which may vary in their complexity [10], [11] and whose general applicability on national level is still being elaborated [II], [12]. The precise specification of the means of calculating the limit of decision should therefore be a part of the analytical instructions. Determination of the limit of decision and determination of an analyte are based, except in the case of absolute methods (gravimetry, cou-lometry). not only on the actual course of the... 

The critical signal value > plays a central part in determining the characteristics of the procedure. Via an experimentally supported or calculated calibration relation (e.g.. Y=ao + a,X) it leads to the limit of decision. Ten, =.vjecision (see Fig. 2). 

The corresponding critical concentration. Vcrii=.Vdei-isi n. limit of decision. is obtained by combining the calibration relation with the expression for Vcrit by assuming that Vbiank = o-... 

Historically, the simple ka criteria used in Figure 2 are based on numerous simplifications. They are usually based on the standard deviation a of blank value measurements The limit of decision is defined with A = 3. the limit of detection with A = 6, and as one possibility, the limit of quantitation with k= 10 [16). (The k values take into consideration the probability ot of erroneous statistical and, therefore, erroneous analytical decisions. Thus, by fixing k or a, the purpose of the particular trace-analytical procedure can be taken into account.) The basic considerations in such definitions of method limits extend back to H. Kaiser (I4J and G. Ehrlich [17], Kaiser also tried to define characteristic quantities of methods for multicomponent analysis. For reasons of space, simultaneous multicomponent analysis cannot be discussed here [ 18]. [ 19]. The previous discussion reveals how delicate results of trace analyses are in general. To achieve a re.sponsible discussion in public it should be at least reported together with... 

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