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182 Modern Analytical Chemistry
sampling plan
A plan that ensures that a representative sample’s purity is often the most important parameter. For example, a material sci-
sample is collected.
SOLUTION
2
The overall variance, s o , is determined using the data on the left and is equal to
–7
2
4.71 ´ 10 . The method’s contribution to the overall variance, s m , is
–8
determined using the data on the right and is equal to 7.00 ´10 . The variance
2
due to sampling, s s , is therefore
2
2
–7
–8
2
s s = s o – s m = 4.71 ´10 – 7.00 ´10 = 4.01 ´10 –7
7 B Designing A Sampling Plan
A sampling plan must support the goals of an analysis. In characterization studies a
entist interested in the surface chemistry of a metal is more likely to select a freshly
exposed surface, created by fracturing the sample under vacuum, than a surface that
has been exposed to the atmosphere for an extended time. In a qualitative analysis
the sample’s composition does not need to be identical to that of the substance
being analyzed, provided that enough sample is taken to ensure that all components
can be detected. In fact, when the goal of an analysis is to identify components
present at trace levels, it may be desirable to discriminate against major components
when sampling. In a quantitative analysis, however, the sample’s composition must
accurately represent the target population. The focus of this section, therefore, is on
designing a sampling plan for a quantitative analysis.
Five questions should be considered when designing a sampling plan:
1. From where within the target population should samples be collected?
2. What type of samples should be collected?
3. What is the minimum amount of sample needed for each analysis?
4. How many samples should be analyzed?
5. How can the overall variance be minimized?
Each of these questions is considered below in more detail.
7 B.1 Where to Sample the Target Population
Sampling errors occur when a sample’s composition is not identical to that of the
population from which it is drawn. When the material being sampled is homoge-
neous, individual samples can be taken without regard to possible sampling errors.
Unfortunately, in most situations the target population is heterogeneous in either
time or space. As a result of settling, for example, medications available as oral sus-
pensions may have a higher concentration of their active ingredients at the bottom
of the container. Before removing a dose (sample), the suspension is shaken to min-
imize the effect of this spatial heterogeneity. Clinical samples, such as blood or
urine, frequently show a temporal heterogeneity. A patient’s blood glucose level, for
instance, will change in response to eating, medication, or exercise. Other systems
show both spatial and temporal heterogeneities. The concentration of dissolved O 2
in a lake shows a temporal heterogeneity due to the change in seasons, whereas
point sources of pollution may produce a spatial heterogeneity.
When the target population’s heterogeneity is of concern, samples must be ac-
quired in a manner that ensures that determinate sampling errors are insignificant.
If the target population can be thoroughly homogenized, then samples can be taken
without introducing sampling errors. In most cases, however, homogenizing the