50
2 Analytical Properties
__ Box2.3
Here is an example of random errors in an analytical process based on gravimetry: the determination of iron in a sample. Each measurement operation involved in this methodology produces a random error that is usually established previously from the characteristics of the
measuring system (instrument) used.
The process is started by weigh ing a solid sample or measuring the volume of a liquid
sample; the measurement will contain a random error of ± 0.0002 g and ± 0.03 mL, respectively.Thus, if the sample weight is 0.5280 g, then the datum will be subject to a fixed random
error, so it should be expressed as 0.5280 ± 0.0002 g.
Since the analytical process involves dissolution and oxidation of iron to Fe h ion, precipitation as Fe(OHh with NH] in the presence of an ammonium salt, filtration through paper,
drying and calcination of the precipitate in a crucible to obtain a weighable form of iron
(Fe10]), the clean, dry crucible to be used must be "tared" (weighed) before it receives the
fil ter paper containing the precipitate. This produces a weighing error of ± 0.0002 g.
After the hydroxide is thermally converted into the oxide (and the paper burnt), the crucible
is cooled down and weighed again, which introduces a new random error of ± 0.0002 g.
Consequently, the analytical process is subject to at least three sources of random errors
that coincide with the three measurements made. These indeterminate errors obviously
affect the final result. Box 2.7 shows the way the random error in the final result is calculated.
Systematic or determinate errors are due to well-defined operational alterations
in the analytical process (e.g. the presence of interferents, incomplete filtration,
carry-over and adsorption losses in trace analyses, deteriorated reagent or standard solutions). They are referred to the true value (X) or that held as true (X')
and materialize in differences (deviations) of the results from them. Systematic
errors affect the analytical property accuracy; a result that is subject to a small
systematic error may be an accurate result. Consequently, deviations are of a definite sign: positive (overestimation) or negative (underestimation). Errors that are
very large are called "gross errors". Systematic errors are constant or proportional
depending on whether or not they depend on the analyte concentration. Also,
they can be ascribed to an individual result (Xi) or to a method characterized by
the mean (X, p') of the results produced by its repeated application to the same
sample. This gives rise to three different designations, namely (Fig. 2.2):
(a) Accuracy proper, when the error refers to a result (in which case it coincides
with the difference [Xi - X'D;
(b) bias, when the error refers to a method that was used to perform n <30
determinations (the difference sought being [X - X'D; and
(c) relative trueness, when the error refers to a method that was used to carry
out n > 30 determinations (the difference being [p' - X'D (see Fig. 2.5).
Gross or spurious errors are essentially similar to systematic errors (see Table
2.1) but considerably larger in magnitude. They are positive or negative errors
that introduce severe alterations in the results (e.g. between -60% and +300%
in relative terms). Gross errors can be easily detected and avoided. Also, they require no special treatment - the results concerned are simply rejected, even
though statistical rules can be used for this purpose (see Box 2.10).
2 Analytical Properties
__ Box2.3
Here is an example of random errors in an analytical process based on gravimetry: the determination of iron in a sample. Each measurement operation involved in this methodology produces a random error that is usually established previously from the characteristics of the
measuring system (instrument) used.
The process is started by weigh ing a solid sample or measuring the volume of a liquid
sample; the measurement will contain a random error of ± 0.0002 g and ± 0.03 mL, respectively.Thus, if the sample weight is 0.5280 g, then the datum will be subject to a fixed random
error, so it should be expressed as 0.5280 ± 0.0002 g.
Since the analytical process involves dissolution and oxidation of iron to Fe h ion, precipitation as Fe(OHh with NH] in the presence of an ammonium salt, filtration through paper,
drying and calcination of the precipitate in a crucible to obtain a weighable form of iron
(Fe10]), the clean, dry crucible to be used must be "tared" (weighed) before it receives the
fil ter paper containing the precipitate. This produces a weighing error of ± 0.0002 g.
After the hydroxide is thermally converted into the oxide (and the paper burnt), the crucible
is cooled down and weighed again, which introduces a new random error of ± 0.0002 g.
Consequently, the analytical process is subject to at least three sources of random errors
that coincide with the three measurements made. These indeterminate errors obviously
affect the final result. Box 2.7 shows the way the random error in the final result is calculated.
Systematic or determinate errors are due to well-defined operational alterations
in the analytical process (e.g. the presence of interferents, incomplete filtration,
carry-over and adsorption losses in trace analyses, deteriorated reagent or standard solutions). They are referred to the true value (X) or that held as true (X')
and materialize in differences (deviations) of the results from them. Systematic
errors affect the analytical property accuracy; a result that is subject to a small
systematic error may be an accurate result. Consequently, deviations are of a definite sign: positive (overestimation) or negative (underestimation). Errors that are
very large are called "gross errors". Systematic errors are constant or proportional
depending on whether or not they depend on the analyte concentration. Also,
they can be ascribed to an individual result (Xi) or to a method characterized by
the mean (X, p') of the results produced by its repeated application to the same
sample. This gives rise to three different designations, namely (Fig. 2.2):
(a) Accuracy proper, when the error refers to a result (in which case it coincides
with the difference [Xi - X'D;
(b) bias, when the error refers to a method that was used to perform n <30
determinations (the difference sought being [X - X'D; and
(c) relative trueness, when the error refers to a method that was used to carry
out n > 30 determinations (the difference being [p' - X'D (see Fig. 2.5).
Gross or spurious errors are essentially similar to systematic errors (see Table
2.1) but considerably larger in magnitude. They are positive or negative errors
that introduce severe alterations in the results (e.g. between -60% and +300%
in relative terms). Gross errors can be easily detected and avoided. Also, they require no special treatment - the results concerned are simply rejected, even
though statistical rules can be used for this purpose (see Box 2.10).