them (so they are all positive), sums them and then selects the values ofmandcthat
give the minimum deviations. The end result of the regression analysis is the equation
for the best-fit straight line for the experimental data set. This is then used to construct
the calibration curve and subsequently to analyse the test analyte(s). Most modern
calculators will carry out this type of analysis and will simultaneously report the 95%
confidence limits for themandcvalues and/or the standard deviation associated with
the two values together with the ‘goodness-of-fit’ of the data as expressed by a
correlation coefficient, ror acoefficient of determination,r^2. The stronger the
correlation between the two variables, the closer the value ofrapproachesþ1or1.
Values ofrare quoted to four decimal places and for good correlations commonly
exceed 0.99. Values of 0.98 and less should be considered with care since even slight
curvature can giver-values of this order.
In the routine construction of a calibration curve, a number of points have to be
borne in mind:- Selection of standard values: A range of standard analyte amounts/concentrations
should be selected to cover the expected values for the test analyte(s) in such a way
that the values are equally distributed along the calibration curve. Test samples should
not be estimated outside this selected range, as there is no evidence that the regression
analysis relationship holds outside the range. It is good practice to establish the
analytical range and the limit of detection for the method. It is also advisable to
determine the precision (standard deviation) of the method at different points across
the analytical range and to present the values on the calibration curve. Such a plot is
referred to as aprecision profile. It is common for the precision to decrease (standard
deviation to increase) at the two ends of the curve and this may have implications for
the routine use of the curve. For example, the determination of testosterone in male
and female serum requires the use of different methods since the two values (reference
range 10–30 nM for males,<3 nM for females) cannot be accommodated with
acceptable precision on one calibration curve. - Use of a ‘blank’ sample: This is one in which no standard analyte is present. One
should be included in the experimental design when possible (it will not be possible,
for example, with analyses based on serum or plasma). Any experimental value,
e.g. absorbance, obtained for it must be deducted from all other measurements.
Example 9(cont.)
An alternative approach to the comparison of the two methods is to plot the two
data sets as anx/yplot and to carry out a regression analysis of the data. If this is done
using the glucose oxidase data as theyvariable, the following results are obtained:
Slope: 1.0016, intercept: 0.1057, correlation coefficientr: 0.9997.
The slope of very nearly one confirms the similarity of the two data sets, whilst the
small positive intercept on they-axis confirms that the glucose oxidase method gives
a slightly higher, but insignificantly different, value to that of the hexokinase
method.34 Basic principles