Agriculture Reference
In-Depth Information
chromatographic conditions. In many instances, a few approaches are combined to
obtain suitable quantitative results [54,55].
cients of determination (
r
2
)
The Role of Weighting Factors for Calibration
Coef
or correlation coef
cients (
r
) have often been used as indicators of linearity for
calibration curves, although they do not guarantee that the calibration curve
ts the
data well, that is, all data points across the curve have good accuracy [38]. In statistics,
calibration curve data can be divided into homoscedastic data and heteroscedastic data.
Homoscedastic data have similar standard deviations for the entire calibration
range [56]. That is, the errors at the low end of the curve are close to the errors at
the high end of the curve.
The calibration curve can be generated using calibration data and expressed using
the following equation:
y
ax
b
(2.5)
where
y
and
x
are the response (signal intensity) and concentration of an analyte,
respectively,
a
is the slope, and
b
is the intercept. The accuracy or error of each data
point can be used to evaluate the quality, that is, linearity, of a calibration curve. The
accuracy and error can be calculated as follows (Eqs. 2.6 and 2.7):
calculated concentration
theoretical concentration
Accuracy
%
100
(2.6)
calculated concentration
theoretical concentration
theoretical concentration
Error
%
100 (2.7)
where calculated concentration is back calculated concentration using the calibration
curve equation. From Equations 2.6 and 2.7,
the error and accuracy have the
following relationship (Eq. 2.8):
Error
%
accuracy
100
(2.8)
In general, either error (%) or accuracy (%) for each data point can be automatically
calculated by the vendors
software to show the quality of a calibration curve when a
calibration curve is generated, that is,
a
,
b
, and
r
2
or
r
are calculated.
For homoscedastic data, curve weighting is not necessary, that is, no weighting or
equal weighting. Therefore, the
r
2
or
r
can be safely used as an indicator of linearity
for the calibration. Higher
r
2
or
r
value is taken to indicate higher accuracy for the
calibration curve.
For heteroscedastic data, however, the standard deviation increases with the
concentration of an analyte. The absolute error is more or less proportional to the
concentration. Because a calibration curve for LC
'
-
MS or GC
-
MS analyses often
covers three to
five orders of magnitude, most of the data are heteroscedastic. In this
case, the value of
r
2
or
r
cannot be used as a unique indicator of linearity. Higher
r
2
or
r
