Figure 2.2
Normal error curves. (a) Curve (a) shows a normal distribution about the true
value. Curve (b) shows the effect of a determinate error on the normal
distribution. (b) Curves showing the results of the analysis of a sample by
two methods of differing precision. Method A is the more precise, or reliable.2.3—
The Evaluation of Results and Methods
A set of replicate results should number at least twenty-five if it is to be a truly representative 'statistical
sample'. The analyst will rarely consider it economic to make this number of determinations and
therefore will need statistical methods to enable him to base his assessment on fewer data, or data that
have been accumulated from the analysis of similar samples. Any analytical problem should be
examined at the outset with respect to the precision, accuracy and reliability required of the results.
Analysis of the results obtained will then be conveniently resolved into two stages – an examination of
the reliability of the results themselves and an assessment of the meaning of the results.
The Reliability of Measurements
When considering the reliability of the results, any determination which deviates rather widely from the
mean should be first investigated for gross experimental or arithmetic error. Except in cases where such
errors are revealed, questionable data should only be rejected when a proper statistical test has been
applied. This process of data rejection presents the analyst with an apparent paradox. If the limits for
acceptance are set too narrowly, results which are rightly part of a statistical sample may be rejected
and narrow limits may therefore only be applied with a low confidence of containing all statistically
relevant determinations. Conversely wide limits may be used with a high confidence of including all
relevant data, but at a risk of including some that have been subject to gross error. A practical
compromise is to set limits at a confidence level of 90% or 95%.
There are two criteria which are commonly used to gauge the rejection of results. Of these, the most
convenient to use is based on the interval