Metrohm viva 1.0 Manual - Manual (Page 606)

5.6 Evaluation subwindow
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viva 1.0
The calculated calibration curve is used with subsequent measurements to
determine the associated result x
M
from the mean value y
̅
M
. The mean
value y
̅
M
and the scattering σ
y,M
of the individual values are defined
thereby as follows:
The estimation of the total error σ
x
of the result x
M
is carried out with a
linear error calculation that takes into account not only the error
amount from the measurement but also that from the calibration.
Because of the fact that the two amounts are statistically independent of
one another, it is not the individual errors
σ that are added but rather
their variances σ 2 (with t = student factor):
The error amount from the measurement itself is calculated from the
derivative of the calibration function resolved in accordance with x in
accordance with y and the measured scattering
σ
y,M
as follows:
The errors of the individual parameters p
i
= a, b, c, d of the calibration
function used are determining for the calculation of the error amount
from the calibration. Because of the fact that these parameters are statisti-
cally dependent on one another, all covariances cov(p
i
, p
j
) must be taken
into account here:
Statistically speaking, only small random samples (<10) are determined for
voltammetric measurements from a population with Gaussian distribution.
These random samples indicate a student distribution that is taken into
account with the student factor t. If the variance is made up of a number
of partial variances, then the student factor is calculated by means of
Welch-Satterthwaite formula approximation. The variance acquired with
this procedure is multiplied by t
2 ; the resulting square root yields the
standard deviation of the result.
The student factor t depends on the number of measurements n, or, to be
more precise, on the number of degrees of freedom n
− f, for which n is