2.5 Basic Analytical Properties
57
I 2.5.1 Precision
The precision concept was previously described in dealing with errors in Analytical Chemistry (Sect. 2.3). In formal terms, precision can be defined as the
"degree of consistency among results obtained by applying the same analytical
method separately to individual aliquots of the same sample» or as the "dispersion of the results with respect to one another and their mean?' Dispersion is the
opposite of precision: the higher the precision, the lower the dispersion. On the
other hand, precision is synonymous with "clustering». As noted earlier, precision is one cornerstone for accuracy.
Precision materializes in random or indeterminate errors. The reference from
which differences or deviations are established is internal, viz. the set of results,
characterized by its mean (X, p'). By contrast, accuracy is referred to an external
landmark eX'). The mathematical support for precision is provided by statistics
(Chemometrics).
Precision is not a unique, isolated concept; rather, it depends on the object to
which it is applied - which gives rise to a variety of statistical parameters - and
on the way the set of results is obtained. Both notions are commented on below.
Precision can be referred to an individual result, all the results or their mean.
The precision of an individual result is defined as the difference between the
result and the arithmetic mean of the set of results. Such a difference coincides
with the systematic error, which can be positive or negative.
d", = ± (X i - p')
In relative terms, the random deviation from a result can be expressed as a fraction of unity or a percentage:
n < 30
n > 30
The quantities used to characterize the precision of a set of results rely on statistical
parameters based on normal (Gaussian) distributions. The higher the precision is,
the smaller the values of such parameters will be as they are directly related to
dispersion. The best known parameter of this type is the standard deviation, which
is described in qualitative terms as the distance (to the left or right) of the mean to
the inflection point in the bell-shaped (Gaussian) curve,and in quantitative terms as
"
- 2
L(Xj - X)
5=
=
a =
n -1
n < 30
n> 30
57
I 2.5.1 Precision
The precision concept was previously described in dealing with errors in Analytical Chemistry (Sect. 2.3). In formal terms, precision can be defined as the
"degree of consistency among results obtained by applying the same analytical
method separately to individual aliquots of the same sample» or as the "dispersion of the results with respect to one another and their mean?' Dispersion is the
opposite of precision: the higher the precision, the lower the dispersion. On the
other hand, precision is synonymous with "clustering». As noted earlier, precision is one cornerstone for accuracy.
Precision materializes in random or indeterminate errors. The reference from
which differences or deviations are established is internal, viz. the set of results,
characterized by its mean (X, p'). By contrast, accuracy is referred to an external
landmark eX'). The mathematical support for precision is provided by statistics
(Chemometrics).
Precision is not a unique, isolated concept; rather, it depends on the object to
which it is applied - which gives rise to a variety of statistical parameters - and
on the way the set of results is obtained. Both notions are commented on below.
Precision can be referred to an individual result, all the results or their mean.
The precision of an individual result is defined as the difference between the
result and the arithmetic mean of the set of results. Such a difference coincides
with the systematic error, which can be positive or negative.
d", = ± (X i - p')
In relative terms, the random deviation from a result can be expressed as a fraction of unity or a percentage:
n < 30
n > 30
The quantities used to characterize the precision of a set of results rely on statistical
parameters based on normal (Gaussian) distributions. The higher the precision is,
the smaller the values of such parameters will be as they are directly related to
dispersion. The best known parameter of this type is the standard deviation, which
is described in qualitative terms as the distance (to the left or right) of the mean to
the inflection point in the bell-shaped (Gaussian) curve,and in quantitative terms as
"
- 2
L(Xj - X)
5=
=
a =
n -1
n < 30
n> 30