7116 ‎(2)‎

• UCREFRP Catalog Number: 7116
• Author: Baxter, G. and J. Simon
• Title: Editor
• USFW Year: Series
• USFW - Doc Type: 1970
• Copyright Material: YES

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Fig. 7. Analogy between shooting result and estimation. The center of the target represents the true population size y, and the
bias the distance between the center of the target and the center E(y) of the shot group. The mean distance between the shots
(dots) and the center of the shot group represents the sampling error SE(y).

confidence interval about the estimate 9. A 95 %
confidence interval has the meaning that the true
(but unknown) y is included in this interval in 95
cases out of 100 if, hypothetically, the estimation
were repeated many times. The calculation of the
confidence interval is often based on the Standard
Error.
Finally a word about the measurement of the
spatial variation of a population. Anyone familiar
with fish sampling has observed that the density
of fish usually varies from site to site. Suppose
that the total area in which the population lives is
divided into a number of smaller units. The mean
density per unit, '1, is then the total population size
divided by the number of units. The (spatial)
variance V(y) ofy is the mean value of the squared
deviations (y - '1) over all units, and the Standard
Deviation SD(y) of y the square root of V(y).
SD(y) is a measurement of how much the popula-
tion size in the units differ, on the average, from
the population mean '1. Observe the similarities
and differences of SE(Y) and SD(y); the former
is a measurement of the precision of an estimate y,

and the latter is a measurement of the spatial
variation of the population. SD(y) and '1 are most
easily calculated using a calculator with pre-
programmed functions.

Precision requirements

In all studies the attempt is, of course, to obtain
as good a precision as possible. The problem is
that increased precision usually has to be paid for
in time, work and money. In addition, the preci-
sion requirement is intimately linked to the type of
question that is to be answered.
As an example, say we are interested in com-
paring the fish densities in two streams. Esti-
mation yields 9 I and 92' respectively. If both
estimates have poor precision, we may not be able
to tell if there is any real difference between the
true densities, unless the estimated difference is
very large. For some purposes, thus, a poor preci-
sion may make the study quite worthless. On the
other hand, if we are interested merely in dis-