Biological field and laboratory methods for measuring the quality of ...

in such a manner that a unit of space may be
used, so that random sampling may be more
easily carried out.
For example, suppose the problem is to
estimate the chlorophyll content of algae in a
pond at a particular time of year. The measurement
is upon algae, yet the sample consists of a
volume of water. We could use our knowledge of
the way the algae are spatially distributed or
make some reasonable assumptions, tnen
construct a random sampling scheme based upon
a unit of volume (liter) as the basic sampling
unit.
It is not always a simple or straightforward
matter to define sampling units, because of the
dynamic nature of living populations. Many
aquatic organisms are mobile, and even rooted
or sessile forms change with time, so that
changes occurring during the study often make
data interpretation difficult. Thus the benefit to
be derived from any attempt to consider such
factors in the planning stage will be considerable.
Random sample selection is a subject apart
from the selection of the study site. It is of use
only after the study objectives have been
defined, the type of measurements have been
selected, and the sampling units have been
defined. At this point, random sampling provides
an objective means of obtaining information
to achieve the objectives of the study.
One satisfactory method of random sample
selection is described. First, number the universe
or entire set of sampling units from which the
sample will be selected. This number is N. Then
from a table of random numbers select as many
random numbers, n, as there will be sampling
units selected for the sample. Random numbers
tables are available in most applied statistics
texts or books of mathematical tables. Select a
starting point in the table and read the numbers
consecutively in any direction (across, diagonal,
down, up). The number of observations, n
(sample size), must be determined prior to
sampling. For example, if n is a two-digit
number, select two-digit numbers ignoring any
number greater than n or any number that has
already been selected. These numbers will be the
numbers of the sampling units to be selected.
To obtain reliable data, information about the
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BIOMETRICS - RANDOM SAMPLING
statistical population is needed in advance of the
full scale study. This information may be
obtained from prior related studies, gained by
pre-study reconnaissance, or if no direct information
is available, professional opinion
about the characteristics of the population may
be relied upon.
2.1.1 Simple random sampling
Simple (or unrestricted) random sampling is
used when there is no reason to subdivide the
population from which the sample is drawn. The
sample is drawn such that every unit of the
population has an equal chance of being
selected. This may be accomplished by using the
random selection scheme already described.
2.1.2 Stratified random sampling
If any knowledge of the expected size or
variation of the observations is available, it can
often be used as a guide in subdividing the
population into subpopulations (strata) with a
resulting increase in efficiency of estimation.
Perhaps the most profitable means of obtaining
information for stratification is through a prestudy
reconnaissance (a pilot study). The pilot
study planning should be done carefully,
perhaps stratifying based upon suspected variability.
The results of the pilot study may be used
to obtain estimates of variances needed to
establish sample size. Other advantages of the
pilot study are that it accomplishes a detailed
reconnaissance, and it provides the opportunity
to obtain experience in the actual field situation
where the final study will be made. Information
obtained and difficulties encountered may often
be used to set up a more realistic study and
avoid costly and needless expenditures. To maximize
precision, strata should be constructed
such that the observations are most alike within
strata and most different among strata, i.e.,
minimum variance within strata and maximum
variance among strata. In practice, the information
used to form strata will usually be from
previously obtained data, or information about
characteristics correlated with the characteristic
of interest. In aquatic field situations, stratification
may be based upon depth, bottom type,
isotherms, and numerous other variables suspected
of being correlated with the character-