Paired intervention analysis in ecology

The paired watershed experiments of Likens and coworkers in the Hubbard Brook Experimental Forest are examples of a classical design in ecology, in which a response in a manipulated unit is compared both to the response in the same unit before manipulation and to the response in an adjacent reference unit that remains undisturbed. Early proponents of this design did not attempt statistical analysis of their results but, more recently, before-after-control-impact analysis and randomized intervention analysis have been used by ecologists to draw statistical inferences from such data. These methods are simply two-sample comparisons (before vs. after) of between-unit differences, with significant results often interpreted as evidence for an effect of the intervention. This approach ignores variation caused by differences between units in the trajectories of the response through time, and it does not take into account possible serial correlation of errors. Consequently, the null hypothesis may be rejected much too often. I develop a new, two-stage analysis method that addresses these shortcomings by correcting for serial correlation and using half-series means to assess temporal variation. Unlike paired intervention analysis, the resulting test has close to the nominal level when the time course of the response is allowed to vary between units, but its power is extremely limited due to the lack of true replication in the design.