106
7 Validation of the Measurement Procedure
7.15 Accuracy and Trueness
According to the definition given earlier, accuracy refers to the true value of a quantity,
which means that without knowing it, it is not possible to evaluate the accuracy of
the measurement. In practice, as the knowledge of true value is not accessed, one
should use the term ‘trueness’ in direct association with a reference value and a
measurement error.
– Trueness: how close to the reference value is to the average of the series of measurements for a given material. Trueness is described by the systematic error of
measurement, which can be expressed as an absolute or relative error.
– The absolute error: the difference between the result of the measurement (usually this is the average value of a series of results obtained under repeatability
conditions) and the reference value. Absolute error is expressed in units of concentration.
– Relative error: proportion of the absolute error value to the reference value; this
can be expressed as a dimensionless value or a percentage.
Assessment of the trueness of the analytical results
– Measure simultaneously the content of analyte in CRM and in the blank sample.
Measurements should be performed with at least several repetitions (10 repetitions minimum
is recommended*);
– Subtract the average value for a blank from the average value for the CRM;
– Calculate the standard deviation of the mean values for both;
– Calculate the standard deviation of determined analyte content (apply the law of propagation);
– Compare the reference value with the laboratory result (visually or with the t-test).
*The recommended number of repetitive values allows the use of sound statistical evaluation.
However, one should be aware that there are situations when this is not possible due to the lack of
a sufficient amount of sample or the high cost of a single measurement
The numerical value of the relative error depends on the content of an analyte;
in most cases, the lower the concentration, the greater the relative error. Although it
depends on the kind of analyte and matrix, the general tendency of most commonly
observed values can be exemplified visually, as presented on Fig. 7.2. This however
should be considered as indicative—regarded as typical for a given range of concentrations. Needless to state, that in specific cases, the relative error can diametrically
differ from those indicated in the illustration.
Precision is the degree of compliance of measurements values for the series of
repetitions, or spread of results around the average value. Precision is described by
the standard deviation, the relative standard deviation, confidence interval or range.
The value of the relative standard deviation depends on the content of an analyte—the lower the concentration, the lower the precision can be. Although it depends
on the kind of analyte and matrix, the general tendency of most commonly observed
values can be exemplified by values listed in Table 7.8. This however should be
7 Validation of the Measurement Procedure
7.15 Accuracy and Trueness
According to the definition given earlier, accuracy refers to the true value of a quantity,
which means that without knowing it, it is not possible to evaluate the accuracy of
the measurement. In practice, as the knowledge of true value is not accessed, one
should use the term ‘trueness’ in direct association with a reference value and a
measurement error.
– Trueness: how close to the reference value is to the average of the series of measurements for a given material. Trueness is described by the systematic error of
measurement, which can be expressed as an absolute or relative error.
– The absolute error: the difference between the result of the measurement (usually this is the average value of a series of results obtained under repeatability
conditions) and the reference value. Absolute error is expressed in units of concentration.
– Relative error: proportion of the absolute error value to the reference value; this
can be expressed as a dimensionless value or a percentage.
Assessment of the trueness of the analytical results
– Measure simultaneously the content of analyte in CRM and in the blank sample.
Measurements should be performed with at least several repetitions (10 repetitions minimum
is recommended*);
– Subtract the average value for a blank from the average value for the CRM;
– Calculate the standard deviation of the mean values for both;
– Calculate the standard deviation of determined analyte content (apply the law of propagation);
– Compare the reference value with the laboratory result (visually or with the t-test).
*The recommended number of repetitive values allows the use of sound statistical evaluation.
However, one should be aware that there are situations when this is not possible due to the lack of
a sufficient amount of sample or the high cost of a single measurement
The numerical value of the relative error depends on the content of an analyte;
in most cases, the lower the concentration, the greater the relative error. Although it
depends on the kind of analyte and matrix, the general tendency of most commonly
observed values can be exemplified visually, as presented on Fig. 7.2. This however
should be considered as indicative—regarded as typical for a given range of concentrations. Needless to state, that in specific cases, the relative error can diametrically
differ from those indicated in the illustration.
Precision is the degree of compliance of measurements values for the series of
repetitions, or spread of results around the average value. Precision is described by
the standard deviation, the relative standard deviation, confidence interval or range.
The value of the relative standard deviation depends on the content of an analyte—the lower the concentration, the lower the precision can be. Although it depends
on the kind of analyte and matrix, the general tendency of most commonly observed
values can be exemplified by values listed in Table 7.8. This however should be