Calibration curve defined

In general, the relationship between input and output of a measuring instmment is a complex function that must be determined by calibration, i.e., by recording the output corresponding to different known values of the input, so that a calibration curve can be obtained. In most cases, the functionality represented by the calibration curve is a mere interpolation of experimental points rather than a predetermined theoretical law. The slope of the calibration curve defines the sensitivity of the measuring instrument in general, the higher the sensitivity, the more accurate is the measurement. 

A calibration curve defines the relation between an analytical signal fP, produced by a definite component of a sample, the analyte, and the amount of this component or its concentration. Calibration curves usually have a linear range - sometimes after the analytical signal has been linearized (Fig. 3.3-14b). If there is a linear relation between the concentration c (or amount) of the sample and the observed signal its slope is called sensitivity 7 ... 

The slope term. Dp, for a calibration with polymer 1 is defined at points a and b on the calibration curve as... 

With the multitude of transducer possibilities in terms of electrode material, electrode number, and cell design, it becomes important to be able to evaluate the performance of an LCEC system in some consistent and meaningful maimer. Two frequently confused and misused terms for evaluation of LCEC systems are sensitivity and detection limit . Sensitivity refers to the ratio of output signal to input analyte amount generally expressed for LCEC as peak current per injected equivalents (nA/neq or nA/nmol). It can also be useful to define the sensitivity in terms of peak area per injected equivalents (coulombs/neq) so that the detector conversion efficiency is obvious. Sensitivity thus refers to the slope of the calibration curve. 

The calibration curve is generated by plotting the peak area of each analyte in a calibration standard against its concentration. Least-squares estimates of the data points are used to define the calibration curve. Linear, exponential, or quadratic calibration curves may be used, but the analyte levels for all the samples from the same protocol must be analyzed with the same curve fit. In the event that analyte responses exceed the upper range of the standard calibration curve by more than 20%, the samples must be reanalyzed with extended standards or diluted into the existing calibration range. 

Figure 5 An example calibration curve. Absorbance is plotted against log (concentration of analyte). The competitive equilibrium binding process results in a sigmoidal curve that is fitted using a four-parameter fit. The IC50 is defined as the concentration of analyte that results in a 50% inhibition of the absorbance...

Detectors are usually conpued in terns of their operational characteristics defined by the nininvin detectable quantity of standards, the selectivity response ratio between standards of different conpositlon or structure, and the range of the linear portion of the detector-response calibration curve. These terns are wid. y used to neasure the perfomance of different chronatographic detectors and were fomally defined in section 1.8.1. 

Peedc-to-peak resolution in SEC can be calculated by the ratio of peak separation at the peak maxiaut to the sum of the baseline peak widths. This general definition of resolution is less useful in SEC, where a measure of the ability of the column to separate solutes of different molecular weight is required. For this purposes, we define a new term, the specific resolution factor, R, which relates peak resolution to sample molecular weight, assuming all measurements are made within the linear region of the molecular weight calibration curve, equation (4.41)... 

The linearity of a method is defined as its ability to provide measurement results that are directly proportional to the concentration of the analyte, or are directly proportional after some type of mathematical transformation. Linearity is usually documented as the ordinary least squares (OLS) curve, or simply as the linear regression curve, of the measured instrumental responses (either peak area or height) as a function of increasing analyte concentration [22, 23], The use of peak areas is preferred as compared to the use of peak heights for making the calibration curve [24],... 

The calibration sensitivity of the analytical method employed is simply determined as the slope of the calibration curve. For example, in the case of methyl paraben, the value of calibration sensitivity obtained was 1.6 mAl I/min///M (Figure 6.22). Analytical sensitivity is defined as the ratio between calibration sensitivity and the value of the standard deviation obtained at each concentration.10 The value of the standard deviation encountered for a concentration of 0.6 //M was 0.1, resulting in an analytical sensitivity for methyl paraben at 0.6 //M of 16 m. II/min///M. As indicated for LOD and LOQ, the values obtained for linearity and sensitivity depend on the analytes employed and the corresponding method and instrumental parameters. For example, Liu et al.9 evaluated the LOD and LOQ for Drug A (released from OROS) for a particular analytical method employing //Pl.C to be 0.5 //g/ml. and 2.0 //g/mL, respectively. 

The characteristic calibration curve is shown in Figure 11.21 on a logarithmic scale, over a range from 30 to 550°C. In the region between 150 and 450°C, the maximum sensitivity is seen. Beyond 500°C, the calibration curve tends to flatten out dramatically, and the sensitivity of measurement achievable in this region is limited, as shown by the dashed line in Figure 11.21, which represents the relative temperature sensitivity of the observed fluorescence lifetime, smx defined as... 

Although Rs values of high Ks compounds derived from Eq. 3.68 may have been partly influenced by particle sampling, it is unlikely that the equation can accurately predict the summed vapor plus particulate phase concentrations, because transport rates through the boundary layer and through the membrane are different for the vapor-phase fraction and the particle-bound fraction, due to differences in effective diffusion coefficients between molecules and small particles. In addition, it will be difficult to define universally applicable calibration curves for the sampling rate of total (particle -I- vapor) atmospheric contaminants. At this stage of development, results obtained with SPMDs for particle-associated compounds provides valuable information on source identification and temporal... 

Fig. 12.3. General appearance of a calibration curve. The upper limit of the linear range is defined by saturation, the lower by memory and chemical background or adsorption. In addition, the noise level plays a role for the detection limit.

Sample analysis data quality. Precision of sample analysis is almost always measured by determining the RSD at two or more concentrations without using a calibration curve. Such data do not include the effects of the calibration process on precision. Bluch better information is given by the relative confidence bandwidth (RGB) defined as ... 

Calibration graphs defined by data with non-negligible error have to be constructed by some kind of smoothing operation. In cases, in which the form of the underlying curve is known a priori, the latter can be approximated by minimizing the squares of deviations. Otherwise a spline function can be used (JJ[, 1 ). The spline function S(x) is constructed to minimize a measure of smoothness defined by... 

The lUPAC Commission for Analytical Nomenclature defines the calibration curve [138] as the dependence of the electromotive force of the given ISE -reference electrode cell on the logarithm of the activity or concentration of the given substance. It is recommended that the potential be plotted on the ordinate (the vertical axis) and the logarithmic function of the activity or concentration on the abscissa (the horizontal axis), with the concentration increasing from the left to the right. 

The rules for level I (screening) assays are shown in Table 13.1. An example of the type of samples where a level I assay could be used is the CARRS samples [85] that can be used for screening NCEs using a rat PK model [vide supra). The concept behind this assay is that it should use a small number of standards and a simple linear extrapolation. For level II assays (see Table 13.2) that might be used for discovery PK studies in preclinical species, a complete standard curve is required. In this case a complete standard curve is defined as 10-15 standards in duplicate assayed with at least five standards used in the final calibration curve. Neither level I nor level II assays require the use of quality control (QC) standards. When a compound is in the lead qualification stage, then a level III assay would be required. As shown in Table 13.3, the main distinction for level III assays is that they are required to include at least six QC standards. As described in Tables 13.1-13.3, these rules show the requirements for how an assay should be set up before the samples are assayed and then these rules describe the acceptance criteria for the assays after they have been performed. 

DEFINE NEW HPOPC CALIBRATION CURVE Calibration Curve No. 12 Coluan Set... 1... 

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