Page 180 - Vogel's TEXTBOOK OF QUANTITATIVE CHEMICAL ANALYSIS

where V represents the appropriate variance. The separate evaluation of both
Vs (the sampling variance) and VA (the analytical variance) may be achieved by
using the analysis of variance procedure (See Section 4.18). A comparison can
be made of the between-sample variance - an estimate of the sampling error -
and the within-sample variance - an estimate of the analytical error.
Example 1. If the sampling error is +3 per cent and the analytical error is
+ 1 per cent, from equation ( 1 ) we can see that the total error s, is given by

s, = = k3.16 per cent
If, in the above example, the analytical error was k0.2 per cent then the
total error s, would be equal to k3.006 per cent. Hence the contribution of
the analytical error to the total error is virtually insignificant. Youden7
has stated that once the analytical uncertainty is reduced to one-third of the
sampling uncertainty, further reduction of the former is not necessary. It is most
important to realise that if the sampling error is large, then a rapid analytical
method with relatively low precision may suffice.
In designing a sampling plan the following points should be considered:'
(a) the number of samples to be taken;
(b) the size of the sample;
(c) should individual samples be analysed or should a sample composed of
two or more increments (composite) be prepared.
If the composition of the bulk material to be sampled is unknown, it is
sensible practice to perform a preliminary investigation by collecting a number
of samples and determining the analyte of interest.
The confidence limits (see Section 4.11) are given by the relationship

where s, is the standard deviation of individual samples, X is the mean of the
analytical results and serves as an estimate of the true mean p, and n is the
number of samples taken.

Example 2. An estimate of the variability of nickel in a consignment of an ore,
based on 16 determinations, was found to be + 1.5%. How many samples
should be taken to give (at the 95 per cent confidence level) a sampling error
of less than 0.5 per cent nickel?
The value 0.5 percent is in fact the difference between the sample mean
X and the actual value p. If this value is represented by E, then equation (2)
may be written as

and, therefore,

From the tables (Appendix 12) the value of t for (n - 1 ), 15 degrees of freedom