Optimum Sample Size to Detect Perturbation Effects: The ...

2 Ortiz
biological population and another different goal could be to assess the putative impacts
or perturbations on these populations. The abstract and outline of the problem of their
work indicate that the authors' principal objective was more than a simple stock evaluation.
The focus of the study was rather on evaluating optimum management strategies
of a particular marine ecosystem.
Even though Mouillot et al. (1999) used an elegant statistical method, one which is
more appropriate to determine population descriptors such as the distribution pattern, it
is unfortunately an incomplete analysis regarding sample size estimation. Although the
authors planned, a priori, to apply an ANOVA design to test the working hypothesis,
they made no reference to the statistical power analysis; this offers better opportunities
for determining the deleterious effects of putative perturbations on the ecological system
under study (Bernstein & Zalinski, 1983; Toft & Shea, 1983; Rotenberry & Wiens,
1985; Gerrodette, 1987; Andrew & Mapstone, 1987; Green, 1989; Peterman, 1990a,
1990b; Peterman & M'Gonigle, 1992; Schlese & Nelson, 1996; Gray, 1996; Ribic &
Ganio, 1996; Underwood, 1981, 1991, 1993, 1994, 1996, 1997; Sheppard, 1999).
Had the authors explored power analysis theory, they would have recognised that
while the variability (dispersion statistics) is an important factor to estimate the sample
size, the magnitude of the perturbation is even more important. Hence, the questions to
be addressed are: How large is the disturbance? How many samples are necessary to
evaluate a putative perturbation?
Moreover, the authors did not introduce the precautionary principle in their analysis.
This principle states that potentially damaging pollution emissions should be reduced
even if there is no scientific evidence to prove a causal link between emissions and effects
(Peterman & M'Gonigle, 1992). Even though this concept is related with a particular
type of perturbation (pollution emissions), it is possible to use it in a more general
way to include other source of perturbations. Therefore, environmental assessment programmes
deserve a deeper analysis including more concepts and tools, and should not
reduce the issue solely to variability coefficients.
The principal objectives of the current work are to describe the statistical power analysis
strategy and to demonstrate, using the results of Mouillot et al. (1999), how its application
helps to improve the estimation of the optimum sample size required under a
perturbation working hypothesis.
Proposedmethodology
1. Statistical power analysis
Statistical power analysis constitutes the most suitable procedure for estimating optimal
sample size (n) starting from a particular working hypothesis. The focus here is on the
probability of correctly detecting an effect (e.g., of a perturbation), that is, rejecting the
null hypothesis (H 0 ) of no effect and accepting H 1 (Dixon & Massey, 1969; Winer,
1971; Cohen, 1988; Sokal & Rohlf, 1995). The power of a test is that probability of
correctly rejecting a false hypothesis, (H 0 ). Power is defined by 1 ± b, b being the probability
of making a Type II error or an incorrect acceptance of H 0 . Power can be calculated
from standard equations and tables (e.g., Dixon & Massey, 1969; Winer, 1971;
Cohen, 1988). It is a function of Type I error (a) or incorrectly rejecting H 0 , the sample