Having established that the standard deviations of two sets of data agree at a reasonable confidence
level it is possible to proceed to a comparison of the mean results derived from the two sets, using the t-
test in one of its forms. As in the previous case, the factor is calculated from the experimental set of
results and compared with the table of critical values (Table 2.3). If texp exceeds the critical value for the
appropriate number of degrees of freedom, the difference between the means is said to be significant.
When there is an accepted value for the result based on extensive previous analysis t is computed from
equation (2.9)
where is the mean of the experimental set, μ the accepted value, s the experimental standard
deviation and N the number of results.
If there is no accepted value and two experimental means are to be compared, t can be obtained from
equation (2.10) with (M + N – 2) degrees of freedom.
where is the mean of M determinations, the mean of N determinations and s the pooled standard
deviation (equation (2.3)).
The Application of Statistical Tests
Table 2.5, together with the subsequent worked examples, illustrates the application of the statistical
tests to real laboratory situations. Equation (2.10) is a simplified expression derived on the assumption
that the precisions of the two sets of data are not significantly different. Thus the application of the F-
test (equation (2.8)) is a prerequisite for its use. The evaluation of t in more general circumstances is of
course possible, but from a much more complex expression requiring tedious calculations. Recent and
rapid developments in desk top computers are removing the tedium and making use of the general
expression more acceptable. The references at the end of the chapter will serve to amplify this point.
Example 2.2
In a series of replicate analyses of a sample the following data (%) were obtained:
In the assessment of these data for reliability the first step of arranging them in rank order has been
carried out.
On inspection 4.20 is rejected as having a gross error, and 7.01 is seen as questionable and requiring to
be tested by the Q-test.