Plotting Calibration Curves

Calibration is the process of establishing the relationship between the instrument signal we measure and the known concentrations of the analyte. There are many ways to establish this relationship, some very specialized. As appropriate, these will be covered in more detail in the 

We will assume that the errors in the measured signal, y, are significantly greater than any errors in the known concentration, x. In this case, the best-fit straight line is the one that minimizes vertical deviations from the line. This is the line for which the sum of the squares of the deviations of the points from the line is the minimum. This fitting technique is called the method of least squares. For a given X , y, and the mty = mx + b, the vertical deviation of y, from y = (y. - y). Each point has a similar deviation, so the sum of the squares of the deviations is 

To obtain the slope m and the intercept b of the best-fit line requires the use of calculus, and the details will not be covered in this text. The results obtained are 

Expressions for the uncertainty in the measured value, y, in the slope, and in the intercept are similar to the expressions for the standard deviation (Equation 1.9). Two degrees of freedom are lost in the expression for the uncertainty in y, because both the slope and intercept have been defined  

Modern computerized analytical instruments have quantitative analysis programs that allow the analyst to specify the calibration standard concentrations, select the curve-fitting mode, and calculate the results of the samples from the calibration curve equation. Many of these programs will rerun outlier standards and samples automatically, flag suspect data, compute precision and recovery of spikes, track reference standards for quality control, and perform many other functions that used to be done manually by the analyst. 

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Plot the observed e.m.f. values against the concentrations of the standard solutions, using a semi-log graph paper which covers four cycles (i.e. spans four decades on the log scale) use the log axis for the concentrations, which should be in terms of fluoride ion concentration. A straight line plot (calibration curve) will be obtained. With increasing dilution of the solutions there tends to be a departure from the straight line with the electrode combination and measuring system referred to above, this becomes apparent when the fluoride ion concentration is reduced to ca 0.2 mg L-1. 

First of all, a Standard Curve or a Calibration Curve is plotted between the reciprocal value (i.e., 1 x %-J radioactivity bound to the antibody) versus the amount of standard for a series of unknowns. Thus, the amount of hapten present in the unknown sample is measured from the plotted calibration curve conveniently. 

The analysis of a range of known concentrations of the test substance is necessary to validate the Beer-Lambert relationship. If the plot of absorbance values against concentration results in a straight line then either of the two previously outlined methods may be used. If, however, the resulting graph shows a curve instead of a straight line then the implication is that the actual value for the molar absorption coefficient is dependent to some extent upon the concentration of the compound and as a result invalidates both methods. In such circumstances a graphical plot (calibration curve) will be needed. 

Obtain unknown specimen results either by reading off a plotted calibration curve or use a computer program to calculate from a fitted curve. 

To run a patient sample, you will need to go through exactly the same deproteination, SFE cartridge extraction, IS addition, mobile phases dilution, and injection steps (Fig. 12.4f). From the peak heights relative to the IS height, we can now quantitate the amount of each drug in the patient s blood. To insure linearity, you may need to dilute our windowed plasma blank and spike it with different levels of each standard and plot calibration curves for each compound, but basically, our methods development is done. 

Plotting calibration curves in quantitative analysis - do not force your calibration line to pass through zero if clearly it does not. There is no reason to assume that the zero value is any more accurate than any other reading you have made. 

Because the peak area response is proportional to the amount of solute, a linear response would be more desirable if quantitation of sample components is required. Linearity can be achieved by plotting calibration curves on a log-log scale as in Eq. (2) ... 

Appendices. Appendices contain details needed to support your results and to be used by people who may continue your work. Make it easy for them by organizing the material under subtitles or sub-appendices listed in the table of contents. Use enough words in appendices to define units and manipulations, but do not worry about smooth text with introductions and transitions. Include data sheets, sample calculations including error propagation, tables of intermediate variables in the calculations, working plots, calibration curves, and all the figures and tables that you did not include in the main body. 

Least-squares plots and coefficient of determination, pp. 102, 106 Using spreadsheets for plotting calibration curves, p. 107 Detection limits, p. 111 Statistics of sampling, p. 113... 

Using Spreadsheets for Plotting Calibration Curves (Section 3.18, Figure 3.9)... 

In all physical methods of measurement used in water analysis it proves advantageous, wherever a linear function exists between concentration c and measured value M within the intended measuring range, to dispense with the use of a plotted calibration curve, thereby avoiding unnecessary errors when reading from the calibration lines. 

Finding the concentration of an analyte in the analyzed sample is done by measuring the analyte peak (height or area). This value (y) is substituted in the calibration equation y = ax + bto find the concentration, or this value is used in the plotted calibration curve to find what concentration the analyte has. 

Plot calibration curves of net optical density against concentration of additive in the ethanol solution used for spectroscopy for both BHT and 2-hydroxy-4-n-octoxy benzophenone. 

FIGURE 10 Actual vs. predicted plot (calibration curve) of the validated concentrations of lactic acid obtained by the PLS model built for the spectral interval 59 alone ( ) and by the PLS model of the whole spectra area ( ) using the respective best number of LVs as seen in Figure 9. The interval 59 model outperforms the global one using only 2 LVs instead of 10. 

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