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Chapter 7 Obtaining and Preparing Samples for Analysis 183

target population is impracticable. Even more important, homogenization destroys
information about the analyte’s spatial or temporal distribution within the target
population.

Random Sampling The ideal sampling plan provides an unbiased estimate of the
target population’s properties. This requirement is satisfied if the sample is collected
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at random from the target population. Despite its apparent simplicity, a true ran- random sample
dom sample is difficult to obtain. Haphazard sampling, in which samples are col- A sample collected at random from the
lected without a sampling plan, is not random and may reflect an analyst’s uninten- target population.
tional biases. The best method for ensuring the collection of a random sample is to
divide the target population into equal units, assign a unique number to each unit,
and use a random number table (Appendix 1E) to select the units from which to
sample. Example 7.3 shows how this is accomplished.

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EXAMPLE .
To analyze the properties of a 100 cm ´100 cm polymer sheet, ten 1 cm ´1 cm
samples are to be selected at random and removed for analysis. Explain how a
random number table can be used to ensure that samples are drawn at random.
SOLUTION
As shown in the following grid, we divide the polymer sheet into 10,000 1 cm ´
1 cm squares, each of which can be identified by its row number and its
column number.
0 1 2 98 99
0
1
2

98
99

For example, the highlighted square is in row 1 and column 2. To pick ten
squares at random, we enter the random number table at an arbitrary point,
and let that number represent the row for the first sample. We then move
through the table in a predetermined fashion, selecting random numbers for
the column of the first sample, the row of the second sample, and so on until all
ten samples have been selected. Since our random number table (Appendix 1E)
uses five-digit numbers we will use only the last two digits. Let’s begin with the
fifth entry and use every other entry after that. The fifth entry is 65423 making
the first row number 23. The next entry we use is 41812, giving the first column
number as 12. Continuing in this manner, the ten samples are as follows:

Sample Row Column Sample Row Column
1 23 12 6 93 83
2 45 80 7 91 17
3 81 12 8 45 13
4 66 17 9 12 92
5 46 01 10 97 52