Metrohm viva 1.1 (ProLab) - Manual (Page 711)

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5 Method
viva 1.1 (for process analysis)
￭￭￭￭￭￭￭￭ 699
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 stan-
dard 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 the number of measuring points and f is the number of estimated
parameters. The Student factor t is defined as follows for a probability of
68.3 %:
n − f t n − f t n − f t Curve type f
1 1.837 6 1.091 15 1.035 y = a + bx 2
2 1.321 7 1.077 20 1.026 y = a + bx + cx 2 3
3 1.197 8 1.067 30 1.017 y = a + bx + dx 4 3
4 1.142 9 1.059 50 1.010
5 1.111 10 1.053 100 1.005
Even though probabilities of 90% and more are usual in statistics, we
select 68.3 % in order to ensure compatibility with the conventional speci-
fication of normally distributed measured values Mean value
± Standard
deviation. With normally distributed values, a standard deviation corre-
sponds to a probability of 68.3 %.
The total error CONCM.ASD of the result CONCM consequently indi-
cates the CONCM
± CONCM.ASD area in which the true value of
CONCM may be expected with a probability of 68.3 %.