Agriculture Reference
In-Depth Information
values do not mean higher accuracy for the calibration curve. This is because the large
standard deviations of the points at the top of the curve dominate the calculation,
meaning that, the value of calibration parameters including slope, intercept, and
r
2
(or
r
) mainly depends on the points at the top of the curve (higher concentration
points) [56].
In order to improve the accuracy, especially for the lower end points of a
calibration curve, a suitable weighting factor, such as 1/
x
or 1/
x
2
, is usually applied
when generating the calibration curve, where
x
represents the concentration of an
analyte. The
F
-test can be used to determine whether the data are homoscedastic or
not, but this is unnecessary because the vendors
tting
function (linear and quadratic) and selection of weighting factors (no weighting, 1/
x
and 1/
x
2
, etc.) to calculate either error or accuracy for each calibration point. Users can
easily select an appropriate weighting factor, which gives the least sum of the absolute
values of the errors for all data points across the calibration curve.
For example, a set of calibration data for analyzing Ac-EEMQRR-amide acquired
by LC
'
software provides the curve-
MS/MS were processed to generate a calibration curve using different
weighting factors: equal weighting (i.e., no weighting), inverse of concentration
(1/
x
), and inverse square of concentration (1/
x
2
), as given in Table 2.2, where
x
represents the concentration of Ac-EEMQRR-amide [38]. Even though correlation
coef
-
cients (
r
) were all greater than 0.999 for the three weighting factors, their errors
were signi
cantly different at the low end of the calibration curve. For example, when
equal weighting (no weighting) was applied, the point of 2.0 ng/ml was not quantifi-
-
able. The errors were 37.4 and 16.4% for points of 10 and 20 ng/ml, respectively.
When the weighting factors 1/
x
and 1/
x
2
were applied, all points were quanti
able and
had lower errors. When the 1/
x
2
weighing factor was applied, the errors were all lower
than 5%. Obviously, the 1/
x
2
weighing factor resulted in the minimum sum of
the absolute values of the error. Therefore, the inverse square of concentration (1/
x
2
)
Table 2.2. The Effects of Weighting Factors for Calibration of Ac-EEMQRR-Amide
Obtained by LC-MS/MS
1/
x
2
(
r
=
0.9997);
a
=
0.00879;
b
=
0.0014
Equal (
r
=
0.9995);
a
=
0.00843;
b
=
0.0384
1/
x
(
r
=
0.9995);
a
=
0.00860;
b
=
0.0325
Weighting
Factor
Theo. ng/ml Cal. ng/ml
Error (%)
Cal. ng/ml
Error (%)
Cal. ng/ml
Error (%)
2.00
NQ
NA
1.79
10.75
1.96
2.08
10.00
6.26
37.43
10.22
2.17
10.22
2.17
20.00
16.72
16.42
20.47
2.33
20.25
1.25
50.00
48.68
2.63
51.85
3.70
50.98
1.97
100.00
100.35
0.35
102.50
2.50
100.62
0.62
200.00
207.83
3.92
208.17
4.08
203.67
1.83
0.80
2.32
4.32
1000.00
992.00
976.83
956.83
Source:
Ref. [38], Table 2, p. 7960. Reproduced with permission of Elsevier Science Ltd.
Note:
Theo. ng/ml: theoretical concentration in ng/ml; Cal. ng/ml: back-calculated concentration in ng/ml.
NQ: not quantifiable; NA: not applicable;
r
: correlation coefficient;
a
: slope,
b
: intercept.
