1.11 Precision and the size of samples
As indicated earlier (see Section 1.10), the power of tests is a function of the sizes
of samples used. In general, the precision of an estimate from a certain sample
is increased as a function of the size of sample. A typical measure of precision
is the standard error, which is (sample variance/size of sample)1/2 and clearly
decreases (so precision increases) as size of sample increases. Wherever possible
(and it is always desirable), a maximal acceptable imprecision should be specified.
It is possible to estimate the variance of the variable being measured and thereby
to calculate how many replicates should be included in a sample to achieve the
necessary precision.
There are, however, several features of design of sampling that help to increase
precision of estimates of abundances of organisms. The first is stratification. Wherever it is possible to make a ‘map’ of abundances (from previous studies in the
literature or from pilot studies) stratification of sampling will often substantially
reduce imprecision. As a simple example, let us suppose that it is generally known
that a particular species of sea urchin is generally more abundant (per box core) in
areas of very coarse sediment than where sediments are finer. Let us suppose that
in the study area, about 25% of the seafloor is composed of coarse sediments, in
several large patches. The remaining areas are finer sediments. There are sufficient
model can be proposed that predation or disturbance by the rays decreases
the number of amphipods. This leads to the hypothesis that areas where rays
are experimentally prevented from entering will develop larger numbers of
amphipods than in corresponding control areas.