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184 Modern Analytical Chemistry

A randomly collected sample makes no assumptions about the target popula-
tion, making it the least biased approach to sampling. On the other hand, random
sampling requires more time and expense than other sampling methods since a
greater number of samples are needed to characterize the target population.

judgmental sampling Judgmental Sampling The opposite of random sampling is selective, or judg-
Samples collected from the target mental sampling, in which we use available information about the target popula-
population using available information
tion to help select samples. Because assumptions about the target population are
about the analyte’s distribution within
included in the sampling plan, judgmental sampling is more biased than random
the population.
sampling; however, fewer samples are required. Judgmental sampling is common
when we wish to limit the number of independent variables influencing the re-
sults of an analysis. For example, a researcher studying the bioaccumulation of
polychlorinated biphenyls (PCBs) in fish may choose to exclude fish that are too
small or that appear diseased. Judgmental sampling is also encountered in many
protocols in which the sample to be collected is specifically defined by the regula-
tory agency.

Systematic Sampling Random sampling and judgmental sampling represent ex-
tremes in bias and the number of samples needed to accurately characterize the tar-
systematic sampling get population. Systematic sampling falls in between these extremes. In systematic
Samples collected from the target sampling the target population is sampled at regular intervals in space or time. For a
population at regular intervals in time or system exhibiting a spatial heterogeneity, such as the distribution of dissolved O 2 in
space.
a lake, samples can be systematically collected by dividing the system into discrete
units using a two- or three-dimensional grid pattern (Figure 7.2). Samples
are collected from the center of each unit, or at the intersection of grid
lines. When a heterogeneity is time-dependent, as is common in clinical
studies, samples are drawn at regular intervals.
When a target population’s spatial or temporal heterogeneity shows a
periodic trend, a systematic sampling leads to a significant bias if samples
are not collected frequently enough. This is a common problem when
sampling electronic signals, in which case the problem is known as alias-
ing. Consider, for example, a signal consisting of a simple sine wave. Fig-
ure 7.3a shows how an insufficient sampling frequency underestimates the
Figure 7.2 signal’s true frequency.
Example of a systematic sampling plan for According to the Nyquist theorem, to determine a periodic signal’s true fre-
collecting samples from a lake. Each solid
dot represents a sample collected from quency, we must sample the signal at a rate that is at least twice its frequency (Fig-
within the sampling grid. ure 7.3b); that is, the signal must be sampled at least twice during a single cycle or
period. When samples are collected at an interval of Dt, the highest frequency that
–1
can be accurately monitored has a frequency of (2 Dt) . For example, if samples are
Nyquist theorem –1
Statement that a periodic signal must be collected every hour, the highest frequency that we can monitor is 0.5 h , or a peri-
sampled at least twice each period to odic cycle lasting 2 h. A signal with a cycling period of less than 2 h (a frequency of
avoid a determinate error in measuring more than 0.5 h ) cannot be monitored. Ideally, the sampling frequency should be
–1
its frequency.
at least three to four times that of the highest frequency signal of interest. Thus, if
an hourly periodic cycle is of interest, samples should be collected at least every
15–20 min.
systematic–judgmental sampling
Systematic–Judgmental Sampling Combinations of the three primary approaches
A sampling plan that combines
4
to sampling are also possible. One such combination is systematic–judgmental
judgmental sampling with systematic
sampling. sampling, which is encountered in environmental studies when a spatial or tempo-