Instant Notes: Analytical Chemistry

The absolute error, EA, in a measurement or result, xM, is given by the equation

EA=xM-xT

where xTis the true or accepted value. Examples are shown in Figure 1where a

200 mg aspirin standard has been analyzed a number of times. The absolute

errorsrange from -4 mg to +10 mg.

The relative error, ER, in a measurement or result, xM, is given by the equation

ER=(xM-xT)/xT

Often, ERis expressed as a percentage relative error, 100ER. Thus, for the aspirin

results shown in Figure 1, the relative error ranges from -2% to +5%. Relative

errors are particularly useful for comparing results of differing magnitude.

Absolute and
relative errors

22 Section B – Assessment of data

Aspirin (mg)

195 200 205 210

Absolute error (EA; mg)

Relative error (ER; %)

–5 0 5 10

–2.5 0 2.5 5

Fig. 1. Absolute and relative errors in the analysis of an aspirin standard.

There are three basic sources of determinateor systematic errorsthat lead to a

biasin measured values or results:

● the analyst or operator;

● the equipment (apparatus and instrumentation) and the laboratory environ-

ment;

● the method or procedure.

It should be possible to eliminate errors of this type by careful observation and

record keeping, equipment maintenance and training of laboratory personnel.

Operator errorscan arise through carelessness, insufficient training, illness or

disability. Equipment errorsinclude substandard volumetric glassware, faulty

or worn mechanical components, incorrect electrical signals and a poor or

insufficiently controlled laboratory environment. Methodor procedural errors

are caused by inadequate method validation, the application of a method to

samples or concentration levels for which it is not suitable or unexpected varia-

tions in sample characteristics that affect measurements. Determinate errors that

lead to a higher value or result than a true or accepted one are said to show a

positive bias; those leading to a lower value or result are said to show a nega-

tive bias. Particularly large errors are described as gross errors; these should be

easily apparent and readily eliminated.

Determinate
errors