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

.

If no < 30, recalculate using t from the tables,
and if ~o > .05, a further calculation is in order:

n=~
l+~
N

(4)

After a sample of size, n, is obtained from the
population, the basic sample statistics may be
calculated. The calculations are the same as for
equations (11) through (15) unless the sample
size, n, is greater than 5 percent of the popula-

tion N. If ~ > .05, a correction factor is used so

that the calculation for the sample variance is:
2 (~Xj)2
D(. -
2 _ (N-n) 1 ---n-
S --
N n-l

The other calculations make use of, S2, as
calculated above, wherever S2 appears in the
formulas.

2.2.2 Stratified random sampling

To compute the sample size required to
obtain an estimate of the mean within a
specified acceptable error, computations can be
made similar to those for simple random
sampling: a probability level must be specified;
an estimate of the variance within each stratum
must be available; and the number of sampling
units in each stratum must be known. Although
this involves a good deal of work, it illustrates
the need for a pilot study and indicates that we
must know something about the phenomena we
are studying if we are to plan an effective
sampling program.
If the pilot study or other sources of informa-
tion have resulted in what are considered to be
reliable estimates of the variance within strata,
the sampling can be optimally allocated to
strata. Otherwise proportional allocation should
be used. Optimal allocation, properly used, will
result in more precise estimates for a given
sample size.
For proportional allocation the calculation for
sample size is:

t2~kSk2
Nd2
n-
- 1 ~ksk2
+-
N2d2

BIOMETRICS - RANDOM SAMPLING

where t = the entry for the desired probability
level from a table of "Student's t" (use 2 for a
rough estimate); Nk = the number of sampling
units in stratum k; sk2 = the variance of stratum
k' N = the total number of sampling units in all
, .
strata; and d = the acceptable error expressed ill
the same units as the observations.
For optimal allocation, the calculation is:
t2(~NkSk)2
N2d2 (7)
n= t2~kSk2
1 + N2d2

(5)

where the symbols are the same as above and

where Sk =~ the standard deviation of
stratum k [see Equations (16) to (19)].
Having established sample size, it remains to
determine the portion of the sample to be
allocated to each stratum.
F or proportional allocation:
nNk
nk=N"" (8)

where nk = the number of observations to be
made in stratum k.
For optimal allocation:

nNkSk (9)
nk = ~kSk

(6)

Sample selection within each stratum is
performed in the same manner as for simple
random sampling.

2.2.3 Systematic random sampling

After the location of a transect line is
selected, the number of experimental units (the
number of possible sampling points) along this
line must be determined. This may be done in
many ways depending upon the particular situa-
tion. Possible examples are the number of square
meter plots of bottom centered along a 100-
meter transect (N = 100); or the meters of
distance along a 400-meter transect as points of
departure for making a plankton haul of some
predetermined duration perpendicular to the
transect. (In the second example, a question of
subsampling or some assumption about local,
homogeneous distribution might arise since the
plankton net has a radius less than one meter).
The interval of sampling, C1 determines sample

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