Figure 2.8
Calibration curve for standard addition; S = unspiked sample;
SS1, SS2, SS3 = spiked samples.as possible. These ensuing results ultimately converge to give an accepted composition for the standard,
which may subsequently be used for the assessment and calibration of various analytical methods.
Standards are exemplified by a range of rock types for geochemistry and bovine liver and kale leaves
for biological analysis.
Plotting Calibration (Reference) Graphs Using the 'Least Squares' Regression Method
An ideal calibration curve (Figure 2.7) is a straight line with a slope of about 45 degrees. It is prepared
by making a sequence of measurements on reference materials which have been prepared with known
analyte contents. The curve is fundamental to the accuracy of the method. It is thus vitally important
that it represents the best fit for the calibration data. Many computer software packages, supplied
routinely with various analytical instruments, provide this facility. It is, however, useful to review
briefly the principles on which they are based.
If the relationship between the signal and the amount of analyte is linear, the method of least squares
may be used to obtain the best straight line through the points. Two important assumptions are made in
doing this. Firstly, that the amount of analyte in the references is known accurately, and that any
variations observed in the measurements originate in the intrinsic variability of the analytical signal.
Secondly, that the convention of plotting the signal on the y-axis, and the amount of analyte on the x-
axis, is followed. It is then possible to calculate the best line on the basis of minimizing the sum of the
squares of the deviations in y from the calculated line. (In mathematically orientated texts these
variations are known as residuals.)
If the straight line is represented by