Environmental power analysis – a new perspective

Power analysis and sample‐size determination are related tools that have recently gained popularity in the environmental sciences. Their indiscriminate application, however, can lead to wildly misleading results. This is particularly true in environmental monitoring and assessment, where the quality and nature of data is such that the implicit assumptions underpinning power and sample‐size calculations are difficult to justify. When the assumptions are reasonably met these statistical techniques provide researchers with an important capability for the allocation of scarce and expensive resources to detect putative impact or change. Conventional analyses are predicated on a general linear model and normal distribution theory with statistical tests of environmental impact couched in terms of changes in a population mean. While these are ‘optimal’ statistical tests (uniformly most powerful), they nevertheless pose considerable practical difficulties for the researcher. Compounding this difficulty is the subsequent analysis of the data and the impost of a decision framework that commences with an assumption of ‘no effect’. This assumption is only discarded when the sample data indicate demonstrable evidence to the contrary. The alternative (‘green’) view is that any anthropogenic activity has an impact on the environment and therefore a more realistic initial position is to assume that the environment is already impacted. In this article we examine these issues and provide a re‐formulation of conventional mean‐based hypotheses in terms of population percentiles. Prior information or belief concerning the probability of exceeding a criterion is incorporated into the power analysis using a Bayesian approach. Finally, a new statistic is introduced which attempts to balance the overall power regardless of the decision framework adopted.