Sources of measurement uncertainty

It is worth reporting the sources of uncertainty in measurement as listed by the ISO Guide:

1

incomplete definition of the measurand; ``

2

imperfect realization of the definition of the measurand;

3

non-representative sampling - the sample measured may not represent the defined
measurand;

4

inadequate knowledge of the effects of environmental conditions on the
measurement, or imperfect measurement of environmental conditions;

5

personal bias in reading analogue instruments;

6

finite instrument resolution or discrimination threshold;

7

inexact values of measurement standards and reference materials;

8

inexact values of constants and other parameters obtained from external sources
and used in the data-reduction algorithm;

9

approximations and assumptions incorporated in the measurement method and
procedure;

10

variations in repeated observations of the measurand under apparently identical
conditions.''

These do not need to be commented upon. Let us just give examples of the first two sources.

1. If one has to measure the gravitational acceleration $g$ at sea level, without specifying the precise location on the earth's surface, there will be a source of uncertainty because many different -- even though `intrinsically very precise' -- results are consistent with the definition of the measurand.^1.2
2. The magnetic moment of a neutron is, in contrast, an unambiguous definition, but there is the experimental problem of performing experiments on isolated neutrons.

In terms of the usual jargon, one may say that sources 1-9 are related to systematic effects and 10 to `statistical effects'. Some caution is necessary regarding the sharp separation of the sources, which is clearly somehow artificial. In particular, all sources 1-9 may contribute to 10, because they each depend upon the precise meaning of the clause ``under apparently identical conditions'' (one should talk, more precisely, about `repeatability conditions'[3]). In other words, if the various effects change during the time of measurement, without any possibility of monitoring them, they contribute to the random error.