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

istic of interest. Stratification is often done on
other bases such as convenience or administra-
tive imperative, but except where these cor-
respond with criteria which minimize the
variation within strata, no gain in precision may
be expected.

Number of Strata

In aquatic biological field studies, the use of
knowledge of biological cause-and-effect may
help define reasonable strata (e.g., thermoclines,
sediment types, etc., may markedly affect the
organisms so that the environmental feature may
be the obvious choice for the strata divisions).
Where a gradient is suspected and where stratifi-
cation is based on a factor correlated to an
unknown degree with the characteristic of
interest, the answer to the question of how
many strata to form and where to locate their
boundaries is not clear. Usually as many strata
are selected as may be handled in the study. In
practice, gains in efficiency due to stratification
usually become negligible after only a few divi-
sions unless the characteristic used as the basis
of stratification is very highly correlated with
the characteristic of interest.

2.1.3 Systematic random sampling
In field studies, the biologist frequently
wishes to use some sort of transect, perhaps to
be assured of including an adequate cross section
while maintaining relative ease of sampling. The
use of transects is an example of systematic
sampling. However, a random starting point is
chosen along the transect to introduce the
randomness needed to guarantee freedom from
bias and allow statistical inference.
The method of placement of the transect
should be given a great deal of thought. Often
transects are set up arbitrarily, but they should
not be. To avoid arbitrariness, randomization
should be employed in transect placement.

2.2 Sample Size

2.2.1 Simple random sampling

In any study, one important early question is
that of the size of the sample. The question is
important because if, on the one hand, a sample
is too large, the effort is wasteful, and if, on the

other hand, a sample is too small, the question
of importance to the study may not be properly
answered.

t

Case 1 - Estimation of a Binomial Proportion

An estimate of the proportion of occurrence
of the two categories must be available. If the
categories are presence and absence, let the
probability of observing a presence be P (0 < P
< I) and the probability of observing an absence
be Q (0 < Q < I, P + Q = I). The second type of
information which is needed is an acceptable
magnitude of error, d, in estimating P (and
hence Q). With this information, together with
the size, n, of the population, the formula for n
as an initial approximation (no), is:

t2PQ
no=y

(1)

The value for t is obtained from tables of
"Student's t" distribution, but for the initial
computation the value 2 may be used to obtain
a sample size, no, that will ensure with a .95
probability, that P is within d of its true value. If
no is less than 30, use a second calculation
where t is obtained from a table of "Student's t"
with no - I degrees of freedom. If the calculation

results in an no, where ~o < .05, no further

calculation is warran ted. Use no as the sample

size. If ~ > .05, make the following computa-

tion:

t

n = no
1 + no-l
N

(2)

Case 2 - Estimation of a Population Mean for
Measurement Data

In this case an estimate of the variance, S2,
must be obtained from some source, and a state-
ment of the margin of error, d, must be ex-
pressed in the same units as are the sample
observations. To calculate an initial sample size:
t2 s2
no =7 (3)

4

t