138
8 Measurement Uncertainty
the range in which the true value should be. In the case of results not demonstrating
any spread, the main basis for the measurement uncertainty is the calibration uncertainty d x equal to the value of scale interval of the measuring device used. It is
assumed that the d x is equal to half of the width of the rectangular distribution and
the standard deviation is
u(x)
d x
√
3
(8.13)
(an estimate of the standard deviation in the uniform distribution). If on the basis
of general knowledge, the symmetrical triangular distribution can be taken, then
u(x)
d x
√
6
(8.14)
The other reason for the measurement uncertainties not showing any spread is the
uncertainty of the experimenter, owing to causes beyond their control. The experimenter is using their own experience and knowledge in order to determine the
uncertainty and the standard uncertainty stemming from it. Often the experimenter’s
standard uncertainty is also estimated on the basis of the rectangular distribution; in
this case:
u(x)
e x
√
3
(8.15)
The data taken from the literature, mathematical tables or values calculated with
the help of a calculator are also burdened with uncertainty. If the value of the experimental standard deviation is not given (if it is given, then the uncertainty u(x) is equal
to that deviation) and there is a lack of any information on the uncertainty, standard
uncertainty is then calculated from the formula, using the rectangular distribution:
u(x)
t x
√
3
(8.16)
When the values of results are characterized by the uniform distribution (rectangular), then the value of single result is assumed to be in the range −a … +a, with an
equal probability; in that case, the value of the standard uncertainty is: a/
√
3 (where
a is half the width of the range −a … +a).
When the values of results are characterized by the triangular distribution (the
value of single result is in the range −a … +a, but the occurrence of the mean value
from the range is the most probable), an, in this case, the value of the standard
uncertainty is a a/
√
6.
8 Measurement Uncertainty
the range in which the true value should be. In the case of results not demonstrating
any spread, the main basis for the measurement uncertainty is the calibration uncertainty d x equal to the value of scale interval of the measuring device used. It is
assumed that the d x is equal to half of the width of the rectangular distribution and
the standard deviation is
u(x)
d x
√
3
(8.13)
(an estimate of the standard deviation in the uniform distribution). If on the basis
of general knowledge, the symmetrical triangular distribution can be taken, then
u(x)
d x
√
6
(8.14)
The other reason for the measurement uncertainties not showing any spread is the
uncertainty of the experimenter, owing to causes beyond their control. The experimenter is using their own experience and knowledge in order to determine the
uncertainty and the standard uncertainty stemming from it. Often the experimenter’s
standard uncertainty is also estimated on the basis of the rectangular distribution; in
this case:
u(x)
e x
√
3
(8.15)
The data taken from the literature, mathematical tables or values calculated with
the help of a calculator are also burdened with uncertainty. If the value of the experimental standard deviation is not given (if it is given, then the uncertainty u(x) is equal
to that deviation) and there is a lack of any information on the uncertainty, standard
uncertainty is then calculated from the formula, using the rectangular distribution:
u(x)
t x
√
3
(8.16)
When the values of results are characterized by the uniform distribution (rectangular), then the value of single result is assumed to be in the range −a … +a, with an
equal probability; in that case, the value of the standard uncertainty is: a/
√
3 (where
a is half the width of the range −a … +a).
When the values of results are characterized by the triangular distribution (the
value of single result is in the range −a … +a, but the occurrence of the mean value
from the range is the most probable), an, in this case, the value of the standard
uncertainty is a a/
√
6.