Statistical power analysis and the precautionary principle

We wish to contribute to a resolution of the debate being carried out in this journal over the appropriateness of what is being called the 'precautionary principle'. This principle states that potentially damaging pollution emissions should be reduced even "when there is no scientific evidence to prove a causal link between emissions and effects" (Ministerial declaration from the 2nd International Conference on the Protection of the North Sea, London, 1987). In an earlier Viewpoint article (Mar. Pollut. Bull. 21, 174-176), Professor Gray suggests that "acceptance of the precautionary principle is entirely an administrative and legislative matter and has nothing to do with science", and that it leads to arguments "that do not have the required objectivity and statistical validity". In contrast, Johnston & Simmonds (Mar. Pollut. Bull. 21, 402) argue that the principle is scientific because it allows regulatory action to occur where "there may be insufficient data to prove harmlessness", and where harm may nevertheless result because the "conventional scientific method is not able to fully or adequately predict impact". Thus, they argue that it should be "a responsibility of the scientific community" to report these situations of inadequate information in order to protect against potentially harmful discharges. Both sides in this debate have, however, neglected to discuss explicitly the concept of statistical power (Dixon & Massey, 1983), an often-forgotten component of the same objective, statistical tradition to which Gray (1990) alludes. Statistical power is the probability that a given experiment or monitoring programme will detect a certain size of effect if it actually exists (say, a 30% reduction in abundance of some indicator species caused by some substance in the water). Statistical power analysis is a well established body of statistical theory (Pearson & Hartley, 1976; Dixon & Massey, 1983; Cohen, 1988) that is used to design experimental and monitoring programmes or evaluate their results (e.g. Skalski & McKenzie, 1982; Berstein & Zalinski, 1983; Green, 1989). Clearly, scientists want such programmes to have high statistical power (usually defined as at least 0.8) but, due to limited budgets, small samples, natural variability, or imprecise sampling methods, power is in practice often low in environmental studies (Vaughan & van Winkle, 1982; de la Mare, 1984; Hayes, 1987; Peterman, 1990). While the authors in the debate over the precautionary principle appear to implicitly recognize the importance of statistical power, their failure to explicitly bring out its relevance has led to omission of several important points from the debate. In the following way, statistical power is an integral part of the normal scientific procedure for testing hypotheses that Gray (1990) mentions. A monitoring programme usually tests a null hypothesis (H0) that a discharge does not affect the indicator species in the biota. Results from some statistical test (say a t-test comparing means from control and treatment plots) will either lead to a rejection of H0 or not. If it is rejected and we conclude that there is an effect, then when no effect of the discharging exists in nature, we commit a type I error (Dixon & Massey, 1983). Scientists normally try to reduce the frequency of such errors by setting a low a value (usually 0.05), below which the P value from the statistical test must fall in order to reject H0. In contrast, if the P value falls above et, we do not reject the H0 of no effect. In this case, if in nature the discharge has an effect, then we commit a type II error by not rejecting the null hypothesis (Dixon & Massey, 1983). The probability of making a type II error is normally symbolized by [3. Statistical power is simply 1-[3, and hence it is the probability of correctly