Linear calibration function

Establishing a calibration function with one single broad distributed sample is an alternative to traditional peak postion calibration of SEC systems with a set of narrow distributed standards. An obvious advantage of this technique is time for peak position calibration elution profiles for the set of standards need to be determined for broad standard calibration the elution profile of one sample needs to be determined only. Establishing a linear calibration function with a broad distributed standard includes startup information [M (true), Mn(true)] and an iterative (repeat.. . until) algorithm ... 

Suitable calibration of instruments used is a fundamental necessity, and it is rarely performed in an appropriate way. Most often, linear calibration functions are regarded... 

In case of a linear calibration function (see Chap. 6), the sensitivity becomes SAA = AyA/AxA and corresponds to the slope b of the calibration straight line see Fig. 7.4a. If the calibration function is a curved line, then the sensitivity will vary according to the analyte amount or concentration as Fig. 7.4b shows. 

Computation Effects Selection of the calibration model will influence results. For example, fitting a linear calibration function to data that are non-linear will result in increased uncertainty in values predicted by using the calibration function. 

Part 1 Statistical evaluation of the linear calibration function... 

Usually linear calibration functions ate preferred. To check for hnearity the easiest thing is a visual check by inspection of the calibration data together with the regression tine. Sometimes non-linearity is so obvious, that no statistical test is required. 

ISO 8466-1 1990 - Calibration and evaluation of analytical methods and estimation of performance characteristics - Part 1 Statistical evaluation of the linear calibration function... 

Abstract Based on the new draft of the EURACHEM/CITAC Guide Traceability in Chemical Measurement , this publication describes how traceability can be achieved for chemical measurements using a linear calibration function. Traceability can be accomplished without larger expenditure, if the measurement is calibrated on the basis of appropriate reference standards and the linear regression employed is selected and... 

For chemical measurements with a linear calibration function, traceability of results can be formally established without great expenditure if the calibration is based on suitable reference standards and the linear regression is performed as shown above and (statistically) validated. The use of reference materials as samples make it possible to establish the traceability of a new analysis protocol by using an existing analysis method. 

The linearity of (a part of) the range should be evaluated to check the appropriateness of the straight-line model. This can be achieved by a graphical evaluation of the residual plots or by using statistical tests. It is strongly recommended to use the residual plots in addition to the statistical tests. Mostly, the lack-of-fit test and Mandel s fitting test are used to evaluate the linearity of the regression line [8, 10]. The ISO 8466 describes in detail the statistical evaluation of the linear calibration function [11]. 

ISO 8466-1, Water Quality - Calibration and Evaluation of Analytical Methods and Estimation of Performance Characteristics- Part 1 the Statistical Evaluation of the Linear Calibration Function, Geneva, ISO, 2001. 

In most cases a linear calibration function can be used, as discussed earlier. It... 

The a coefficients have to be calculated using regression procedures. In the case of a calibration function of a higher degree, the calibration graph is curved. The latter also can be approximated by a polygone, where different linear calibration functions are used for well-defined concentration ranges. 

Figure 8.10 A simple example (linear calibration function with intercept A = 0) demonstrating the effects of both noise (or background) and sensitivity (5, Equation [8.61]) on the error propagation when predicting the content (concentration or amount of analyte) from the noisy signal by projecting the Y-axis onto the content axis (x-axis) through the calibration line. A low noise level combined with a high sensitivity S (slope of calibration line) will thus allow small changes in concentration (or amount) to be detectable, and by extension lead to a lower LOD (Equation [8.61]) this is the origin of the more colloquial use of the term sensitivity to indicate lower LOD (and possibly LLOQ) values.

In any case, linear calibration functions should be obtained over two decades with correlation coefficients (R ) better than 0.999 (Figure 26.13). It did not make a difference, if calibration solution were prepared on matrix extracts [28]. 

Good separation of propafenone hydrochloride from the degradation products was obtained and the received values of retardation factors were as follows for propafenone hydrochloride Rp 0.64, and for the degradation products 0.43, 0.82, and 0.88. The elaborated method was validated using ICH guidelines. The linear calibration function was obtained with respect to the peak area in the concentration range of 0.1-3.2 j,g spor, respectively. The limits of detection and quantification were, respectively, 0.02 and 0.08 pg per band. 

In most cases, a linear calibration function can be used (see Section 21.3.1). If c,- is the concentration of a standard sample and. v, is the radiation intensity, absorption, or ion current for the element to be determined, the linear regression has the form ... 

The coefficients a are calculated by regression procedures. Alternatively, different linear calibration functions may be used for different concentration ranges. 

Method Characteristic Parameters of a Linear Calibration Function... 

The measure for sensitivity results from the change in the measuring value when changing concentration. While in a linear calibration function sensitivity corresponds to the regression coefficient b, in a curved calibration function it depends on the respective concentration value and, therefore, corresponds to the first derivation of the calibration function ... 

For the practical determination of the detection criteria, the standard deviation Syo of the blank value Jq or the standard deviation of the intercept a of the linear calibration function is used, where the standard deviation should be calculated from at least = 6 measuring values. The detection criteria is then regarded as the upper limit of the blank value scatter... 

In some special analyses it may be necessary to extend the absorbance measurements beyond the linear range (i.e., beyond the validity of Beer-Lamberts s law). In these cases a non-linear calibration curve has to be generated by measuring concentrations versus spectrophotometer readings. The sample concentrations are then calculated according to the non-linear calibration function or corresponding correction terms applied to the linearly calculated sample concentrations. 

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