Standard deviation calibration-curve detection

External standardization is obtained by constructing a calibration curve, i.e., from plotting measured intensities versus rising concentration of the target compound. Calibration curves are generally linear over a wide range of concentrations. When concentration approaches the detection limit (Chap. 5.2.3) the graph deviates from... 

The beauty of this completely random approach to the analyte detection limit is the direct applicability of the statistical hypothesis testing formalism. Also, long-term trends in calibration slope or backgrounds have little influence. One important assumption is made that the form of the calibration curve [Equation 2c] is fixed. Also, a subtle change has occurred, the operation is no longer linear, with A in the denominator. Thus, the distribution of x is only asymptotically normal, as the relative standard deviation of becomes smaller. 

Sensitivity can be associated with the slope of the calibration curve. It is also dependent on the standard deviation of the measurements. The higher the slope of your calibration curve the higher the sensitivity of your detector for that particular component, but high fluctuations of your measurements will decrease the sensitivity. The more selective the detection, the lower is signal/noise and the higher the sensitivity. The detector response is linear if the difference in response for two concentrations of a given compoimd is proportional to the difference in concentration of the two samples. 

The lower limit of detection given in Equation 5-5 is 3s/m, where s is the standard deviation of a low-concentration sample and m is the slope of the calibration curve. The standard deviation is a measure of the noise (random variation) in a blank or a small signal. When the signal is 3 times as great as the noise, it is readily detectable, but still too small for accurate measurement. A signal that is 10 times as great as the noise is defined as the lower limit of quantitation, or the smallest amount that can be measured with reasonable accuracy. 

A typical chromatogram obtained using this method is shown in Figure 12, and the retention times (Rt) and the relative retention time (Rrt) for pantoprazole sodium and some of its related compounds are shown in Table 6. The calibration curve for the assay determination, obtained over a concentration range of228-670 pg/mL, was found to be linear with a correlation coefficient of0.999. The recovery and relative standard deviation for various assays were 97.3-101.5 and 1.1, respectively. A calibration curve was also developed for pantoprazole sodium related compounds, covering a concentration range of 1 to 3 pg/mL, and which was found to be linear with a correlation coefficient of more than 0.999. The limits of detection and limits of quantitation were calculated as 0.15 pg/mL and 0.49 pg/mL, respectively. 

Fig. 4.16 shows a typical chromatogram for a standard 42pg L 1 phosphate solution and hypoxanthine peaks resulting from various phosphate samples after reaction with the enzyme. The calibration curve had a slope of 0.043 0.002 and an intercept of 0.124 0.033 with a correlation coefficient of 0.998. Linearity up to 30mg L 1 was observed. Relative standard deviation of triplicate runs was 10% or less. The detection limit, twice the signal of the blank, was determined to be 1.5mg L 1. 

One such chelate spray reagent prepared by mixing SAQH (II) and manganous chloride was used successfully to detect organothiophosphorus pesticides on tic with a detection limit of 0.02 Ug/spot (18). Linear calibration curves were obtained up to 6 Ug per spot and the relative standard deviation for O.lug... 

If the slopes of both curves do not differ significantly [t(b) < t s with d.f. = ns + rca — 4], matrix effects are not present and a standard-solution-based calibration line may be used. It is noted that, for calibration lines having a very small residual standard deviation (Sy), matrix interferences have often been detected based on the statistical significance while the lines are nearly parallel. The contribution of the error of this small matrix effect is often negligible compared to the total measurement error. Therefore, it is strongly recommended to perform a visual interpretation of the parallelism of the lines in conjunction with this t-test. 

To determine the limit of detection (LOD) and the limit of quantitation (LOQ), the method based on the residual standard deviation of a regression line and slope was adopted. To determine the LOD and LOQ, a specific calibration curve was studied by using samples containing the analytes in the range of the detection limit and the quantitation limit. The limits of detection for metformin and glibenclamide were 0.013 and 0.007 pg/mL, respectively, and the limits of quantitation were 0.040 and 0.021 pg/mL, respectively. 

The calibration sensitivity does not indicate what concentration differences can be detected. Noise in the response signals must be taken into account to be quantitative about what differences can be detected. For this reason, the term analytical sensitivity is sometimes used. The analytical sensitivity is the ratio of the calibration curve slope to the standard deviation of the analytical signal at a given analyte concentration. The analytical sensitivity is usually a strong function of concentration. 

The detection limit (DL) is the smallest concentration that can be reported with a certain level of confidence. Every analytical technique has a detection limit. For methods that employ a calibration curve, the detection limit is defined as the analyte concentration yielding a response of a confidence factor k higher than the standard deviation of the blank, as given in Equation 8-22. 

Fig. 1 Sample Phosphate standard calibration curve. ODess values are plotted against phosphate concentration in 6 pi assay volume, and the data fitted linearly. Slope is 0.017 0.0002, standard deviation of the background control is 0.0077, and the limit of detection (LOD) is 1.4 pM...

Calibration curve showed good linear relationship (r=0.9998) between artemisinin concentration and CL intensity. The detection limit at S/N ratio of 3 was 5 /tmol/L (100 pmol/injection). The reproducibility of the proposed method was determined using 1 mmol/L and 0.25 mmol/L artemisinin, the relative standard deviation for within-day (n=5) and between-day (n=3) analysed were < 3% and < 11%, respectively. 

LOQ) will typically be higher than the instrumental detection limit (IDL), because of background analyte and matrix-based interferences. The BEC (blank equivalent concentration) used in Table 4.7 is the apparent concentration of an analyte normally derived from intercepted point of its calibration curve or by reference of the actual counts for that analyte in a blank solution. The BEC gives a good indication of the blank level, which will affect the IDL. Most often, the detection limits are calculated as three times the normal standard deviation of the BEC in a within batch replicate analytical measurement of a blank solution. Therefore, if the instrument is stable enough, this will give a better IDL than the BEC itself. The BEC is a combination of the contamination of the analyte in the solution, the residual amount of the analyte in the spectrometer and the contribution of any polyatomic species in the analyte mass. 

Calibration curves were prepared with a standard mixture of thiols according to the labeling procedure and good correlations were observed between the CL intensity as peak height ratio and concentration of thiols up to 500 pmol/injection. The detection limits of standard thiols ranged from 0.23 to 0.30 pmol/injection at a signal-to-noise ratio (S/N) of 3. The repeatability of the proposed method was examined at the 50 pmol/injection level for thiols. The relative standard deviations (RSD) for within-day (n = 3) and between-day (n = 3) runs were < 4.6 and 4.9%, respectively. This method was successfully applied to the determination of thiols in human serum. A typical chromatogram of the extract from human serum determined by the proposed HPLC-CL method is shown in Fig. 3(B). 

Analytical characteristics. Calibration curve was obtained for the determination of SPAX under the optimal experimental conditions. It gives a linear range from 7.0X10" 12 to 4.0X10"8 mol/L with the limit of detection (LOD) as defined by IUPAC, CLod= 3 Sb/m (where Sb is the standard deviation of the blank signals and m is the slope of the calibration graph) was found to be 1.2X1 O 12 mol/L (s/n=3). The relative standard deviation of l.OXiO"7 mol/L SPAX was found to be 1.6% (n = 11). 

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