Environmental Engineering Reference
In-Depth Information
When there is no good basis for assuming a particular parametric distribution,
non-parametric bootstrapping
can be used. In this approach, the data are allowed
to define their own distribution by random resampling. For example, here is a sim-
ple bootstrap procedure for calculating the confidence interval for a mean:
●
Given
k
data points (e.g. the numbers of individuals in a sample of plots),
pick a random selection of them. The new 'virtual' sample should contain
exactly
k
data points, but sampled with replacement, so that some may
appear more than once in the new sample, while others do not appear at all.
●
Estimate mean abundance from the new sample, and keep a note of this value.
●
Repeat this many times (typically at least 1000 replicates are used).
●
The 2.5% and 97.5% percentiles of the resampled abundance estimates then
give the 95% confidence interval.
A related non-parametric approach,
randomisation
, can be used to test whether
two means are significantly different from one another. Here's one way to do this:
●
Randomly re-assign each raw value to one of the two categories, preserving
the sample size of each category (a process known as permutation).
●
Calculate the difference between category means for the permuted sample.
●
Repeat this many times, storing the difference between means each time.
●
Count the number of permuted differences that are more extreme than the
observed difference (either more negative or more positive than absolute
value) and divide by the total number of permutations. This is the approxi-
mate probability that the observed difference could have arisen by chance,
and is equivalent to the
p
-value of standard statistical tests.
There are many variations and elaborations of these randomisation approaches.
For a simple introduction, including software application, see Howell (2007). A
comprehensive text is provided by Manly (1997).
When designing a survey, it is important to understand the possible sources of
bias and poor precision in order to avoid them. Below are some of the key practical
considerations.
●
Ensure that your sample is representative by either
random sampling
, for exam-
ple, a study area might be divided into blocks on a map, each block assigned a
number and sample blocks selected by picking random numbers using a ran-
dom number generator, or
systematic sampling
, for example, covering the
whole study area with points on a grid system, or with transects running paral-
lel to one another. Care is needed with this approach to ensure that the sampling
pattern is not aligned with variation in the population (for example, if transects
run along landscape features that also influence abundance). Randomised start-
ing points and/or directions can help to achieve this. The important point here
is that locations should not be rejected or avoided simply because they might be
hard to access or yield disappointingly few observations.
