2.2—
The Nature and Origin of Errors
On the basis of their origin, errors may usually be classified as determinate or indeterminate. The first
are those having a value which is (in principle at least) measurable and for which a correction may be
made. The second fluctuate in a random manner and do not have a definite measurable value.
Determinate errors may be constant or proportional. The former have a fixed value and the latter
increase with the magnitude of the measurement. Thus their overall effects on the results will differ.
These effects are summarized in Figure 2.1. The errors usually originate from one of three major
sources: operator error; instrument error; method error. They may be detected by blank determinations,
the analysis of standard samples, and independent analyses by alternative and dissimilar methods.
Proportional variation in error will be revealed by the analysis of samples of varying sizes. Proper
training should ensure that operator errors are eliminated. However, it may not always be possible to
eliminate instrument and method errors entirely and in these circumstances the error must be assessed
and a correction applied.
Figure 2.1
The effects of constant and
proportional errors on a
measurement of concentration.Indeterminate errors arise from the unpredictable minor inaccuracies of the individual manipulations in
a procedure. A degree of uncertainty is introduced into the result which can be assessed only by
statistical tests. The deviations of a number of measurements from the mean of the measurements
should show a symmetrical or Gaussian distribution about that mean. Figure 2.2 represents this
graphically and is known as a normal error curve. The general equation for such a curve is
where μ is the mean and σ is the standard deviation. The width of the curve is determined by σ, which
is a useful measure of the spread or precision of a set of results, and is unique for that set of data. An
interval of μ ± σ will contain 68.3% of the statistical sample, whilst the intervals μ ± 2 σ and μ ± 3 σ will
contain 95.5% and 99.7% respectively.