9597

• UCREFRP Catalog Number: 9597
• Author: U.S. Environmental Protection Agency.
• Title: Biological Field and Laboratory Methods for Measuring the Quality of Surface Waters and Effluents.
• USFW Year: 1973.
• USFW - Doc Type: Cincinnati, OH.
• Copyright Material: NO

BIOLOGICAL METHODS

size: n = N/C. The mean is estimated as usual;
the variance as for a simple random sample if
there are no trends, periodicities, or other non-
random effects.

2.3 Subsampling

Situations often arise where it is natural or
imperative that the sampling units are defined in
a two-step manner. For example: colonies of
benthic organisms might be the first step, and
the measurement of some characteristic on the
individuals within the colony might be the
second step; or streams might be the fITst
(primary) step, and reaches, riffles or pools as
the second step (or element) within the unit.
When a samp Ie of primary units is selected, and
then for each primary unit a sample is selected
by observing some element of the primary unit,
the sampling scheme is known as subsampling or
two-stage sampling. The computations are
straight forward, but somewhat more involved.
The method of selection of the primary units
must be established. It may be a simple random
sample (equal probabilities), a stratified random
sample (equal probabilities within strata), or
other scheme such as probability proportional to
size (or estimated size) of primary unit. In any
case, let us call the probability of selection of
the i~~ primary unit, Zj. For simple random

sampling, Zi = ~, where N is the number of

primary units in the universe. For stratified

random sampling, Zki = ~k' where k signifies the

k~~ stratum. For selection in which the primary
units are selected with probability proportional
to their size, the probability of selection of the
.th. . .
J~ pnmary UTIlt IS
Lj
Zj = -;-
kLi
i = 1

(10)

where L equals the number of elements in the
primary unit indicated by its subscript. If
stratification is used with the latter scheme,
merely apply the rule to each stratum. Other
methods of assigning probability of selection
may be used. The important thing is to establish
the probability of selection for each primary
unit.

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3.0 GRAPIDC EXAMINATION OF DATA

Often the most elementary techniques are of
the greatest use in data interpretation. Visual
examination of data can point the way for more
discriminatory analyses, or on the other hand,
interpretations may become so obvious that
further analysis is superfluous. In either case,
graphical examination of data is often the most
effortless way to obtain an initial examination
of data and affords the chance to organize the
data. Therefore, it is often done as a first step.
Some commonly used techniques are presented
below. Cell counts (algal cells per milliliter) will
serve as the numeric example (Table I ).

3.1 Raw Data

As brought out in other chapters of this
manual, it is of utmost importance that raw data
be recorded in a careful, logical, interpretable
manner together with appropriate, but not super-
fluous, annotations. Note that although some
annotations may be considered superfluous to
the immediate intent of the data, they may not
be so for other purposes. Any note that might
aid in determining whether the data are
comparable to other similar data, etc., should be
recorded if possible.

3.2 Frequency Histograms

To construct a frequency histogram from the
data of Table I, examine the raw data to deter-
mine the range, then establish intervals. Choose
the intervals with care so they will be optimally
integrative and differentiative. If the intervals
are too wide, too many observations will be
integrated into one interval and the picture will
be hidden; if too narrow, too few will fall into
one interval and a confusing overdifferentiation
or overspreading of the data will result. It is
often enlightening if the same data are plotted
with the use of several interval sizes. Construct
the intervals so that no doubt exist as to which
interval an observation belongs, i.e., the end of
one interval must not be the same number as the
beginning of the next.
The algal count data in Tables 2 and 3 were
grouped by two interval sizes (10,000 cells/ml
and 20,000 cells/ml} It is,easy'to, see that the data
are grou ped largely in the range 0 to 6 x 104
cells/ml and that the frequency of occurrence is

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