50
Accuracy (by adapting the VIM: JCGM, 2012: 2.13, modified in reference to
ISO, 1994: 3.6) is the closeness of agreement between a measured value and an
accepted reference value. If measurement is modeled as affected by errors, accuracy
is inversely related to errors. The accuracy of a measuring instrument is evaluated in
test conditions, by somehow combining its precision and trueness with respect to a
reference value taken from an available calibrated measurement standard in the process of metrological confirmation of the instrument.
8
An accurate instrument is
exactly what we would like to have: an instrument that produces trustworthy values.
As is discussed at further length in Sect. 4.3, in the human sciences one encounters the term “validity”. In its earliest usages, which are still common in some areas
of the literature, “validity” refers to closeness of agreement between measured values and a true value, sometimes operationalized in terms of an accepted reference
value, as discussed in Sect. 4.3.1. Thus from this perspective the early version of
“validity” is a near synonym of “accuracy”.
Given this sketch of a framework about the characterization of the quality of
process of measuring, the issue arises of whether the quality of measurement results
is entirely and solely determined by the quality of the measurement that produced them.
3.2.2 The Error Approach (or True Value Approach)
Appropriate applications of the empirical strategy mentioned in the opening of Sect.
3.2 generally result in improvements of the behavior of measuring instruments, and
consequently reductions in the variability of their results. Extrapolating from this,
one might suppose that, if this improvement process were to continue indefinitely, a
single, definite value would actually be obtained: “by analyzing the meaning of the
obtained results of measurement, the experimenter ponders on the true value, the
value that the best possible instrument would have generated” (translated from
Idrac, 1960, emphasis added). Indeed, this hypothesis has a simple statistical basis.
To see this, assume that the measurement is repeatable—that is, that (a) the environment and the measuring instrument are sufficiently stable and (b) the observed variability between interactions is only due to the influence of small, independent
causes. Then, the repeated interaction of the instrument with the measurand generates a sample of values whose distribution becomes more and more stable as the
number of values increases. More specifically, if the values can be averaged in a
meaningful way (hence this obviously does not apply to nominal and ordinal properties), and s is the sample standard deviation, it is well known that the standard
deviation of the sample mean is estimated by s n
/
, where n is the sample size. By
increasing the sample size, i.e., repeating the number of interactions of the measuring
8 What is commented above about the trueness of measurement results also applies to accuracy: the
accuracy of measurement results “is not a quantity” (JCGM, 2012: 2.13, Note 1).
3 Technical and cultural contexts for measurement systems
Accuracy (by adapting the VIM: JCGM, 2012: 2.13, modified in reference to
ISO, 1994: 3.6) is the closeness of agreement between a measured value and an
accepted reference value. If measurement is modeled as affected by errors, accuracy
is inversely related to errors. The accuracy of a measuring instrument is evaluated in
test conditions, by somehow combining its precision and trueness with respect to a
reference value taken from an available calibrated measurement standard in the process of metrological confirmation of the instrument.
8
An accurate instrument is
exactly what we would like to have: an instrument that produces trustworthy values.
As is discussed at further length in Sect. 4.3, in the human sciences one encounters the term “validity”. In its earliest usages, which are still common in some areas
of the literature, “validity” refers to closeness of agreement between measured values and a true value, sometimes operationalized in terms of an accepted reference
value, as discussed in Sect. 4.3.1. Thus from this perspective the early version of
“validity” is a near synonym of “accuracy”.
Given this sketch of a framework about the characterization of the quality of
process of measuring, the issue arises of whether the quality of measurement results
is entirely and solely determined by the quality of the measurement that produced them.
3.2.2 The Error Approach (or True Value Approach)
Appropriate applications of the empirical strategy mentioned in the opening of Sect.
3.2 generally result in improvements of the behavior of measuring instruments, and
consequently reductions in the variability of their results. Extrapolating from this,
one might suppose that, if this improvement process were to continue indefinitely, a
single, definite value would actually be obtained: “by analyzing the meaning of the
obtained results of measurement, the experimenter ponders on the true value, the
value that the best possible instrument would have generated” (translated from
Idrac, 1960, emphasis added). Indeed, this hypothesis has a simple statistical basis.
To see this, assume that the measurement is repeatable—that is, that (a) the environment and the measuring instrument are sufficiently stable and (b) the observed variability between interactions is only due to the influence of small, independent
causes. Then, the repeated interaction of the instrument with the measurand generates a sample of values whose distribution becomes more and more stable as the
number of values increases. More specifically, if the values can be averaged in a
meaningful way (hence this obviously does not apply to nominal and ordinal properties), and s is the sample standard deviation, it is well known that the standard
deviation of the sample mean is estimated by s n
/
, where n is the sample size. By
increasing the sample size, i.e., repeating the number of interactions of the measuring
8 What is commented above about the trueness of measurement results also applies to accuracy: the
accuracy of measurement results “is not a quantity” (JCGM, 2012: 2.13, Note 1).
3 Technical and cultural contexts for measurement systems