Statistical methods blank values

Statistical methods provide tools for assessing univariate data (replicate measurements of a single parameter) resulting in measurements of i) accuracy, defined as the difference between an experimental value and the true value the latter is generally not known for a real-world analytical sample, so that accuracy must be estimated using a surrogate sample e.g., a blank matrix spiked with a known amount of analytical standard) ii) precision, such as the relative standard deviation (RSD, also known as the coefficient of variance, COV or CV) iii) methods for calculation of propagation of experimental error in calculations. 

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... 

The limit of quantitation (LOQ) of a method is also given as a quantity of substance or concentration in the substance domain. This limit incorporates the calibration and thus also the uncertainty (error consideration) of the measurements (Ebel and Kamm 1983). Unlike the LOD it is guaranteed statistically and gives the lower limiting concentration which can be unambiguously determined quantitatively. It can differ significantly from the blank value (Montag, 1982 ISO 11843,1997). 

Estimated DL values for the 24 PAH analytes were obtained as follows. Six (empty bottle) procedural blank samples were analyzed in a parallel study, yielding concentration values for an equivalent 0.5 L water sample. The SE values were multiplied by the one-sided critical value of the Student s t-distribution (t.01[5j) statistic to obtain an estimate of the upper 99 percent confidence limit for the actual concentration. This upper limit value was accepted as the estimated detection limit of the method (Table 1). However, we elected not to quantify concentrations below 0.1 ng/L (procedural blank values <0.1 ng/L were not used to obtain net concentrations). 

Accuracy is the term used to describe the degree of deviation (bias) between the (often unknown) true value and what is found by means of a given analytical method. Accuracy cannot be determined by statistical means the test protocol must be devised to include the necessary comparisons (blanks, other methods). 

Two aspects are important for IQC (1) the analysis of control materials such as reference materials or spiked samples to monitor trueness and (2) replication of analysis to monitor precision. Of high value in IQC are also blank samples and blind samples. Both IQC aspects form a part of statistical control, a tool for monitoring the accuracy of an analytical system. In a control chart, such as a Shewhart control chart, measured values of repeated analyses of a reference material are plotted against the run number. Based on the data in a control chart, a method is defined either as an analytical system under control or as an analytical system out of control. This interpretation is possible by drawing horizontal lines on the chart x(mean value), x + s (SD) and x - s, x + 2s (upper warning limit) and x-2s (lower warning limit), and x + 3s (upper action or control limit) and x- 3s (lower action or control limit). An analytical system is under control if no more than 5% of the measured values exceed the warning limits [2,6, 85]. 

In principle, all performance measures of an analytical procedure mentioned in the title of this section can be derived from a certain critical signal value, ycrit. These performance measures are of special interest in trace analysis. The approaches to estimation of these measures may be subdivided into methods of blank statistics , which use only blank measurement statistics, and methods of calibration statistics , which in addition take into account calibration confidence band statistics. 

In radioanalytical chemistry, the critical value can be calculated by either of two common approaches. One is based on repeated measurements of blank samples, and the other on the assumption of Poisson counting statistics. The former method is generally applicable to any measurement process for which the distribution of measurement results is approximately normal. The latter method is useful when the Poisson assumption is valid, but it may give misleading results in other situations. 

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