Detecting cumulative watershed effects: the statistical power of pairing

The statistical power for detecting change in water quality should be a pri mary consideration when designing monitoring studies. However, some of the standard approaches for estimating sample size result in a power of less th an 50%, and doubling the pre- and post-treatment sample size are necessary to increase the power to 80%, The ability to detect change can be improved by including an additional explanatory variable such as paired watershed me asurements. However, published guidelines have not explicitly quantified th e benefits of including an explanatory variable or the specific conditions that favor a paired watershed design. This paper (1) presents a power analy sis for the statistical model (analysis of covariance) commonly used in pai red watershed studies; (2) discusses the conditions under which it is benef icial to include an explanatory variable; and (3) quantifies the benefits o f the paired watershed design. The results show that it is beneficial to in clude an explanatory variable when its correlation to the water quality var iable of concern is as low as about 0.3. The ability to detect change incre ases nonlinearly as the correlation increases. Power curves quantify sample size requirements as a function of the correlation and intrinsic variabili ty. In general, the temporal and spatial variability of many watershed-scal e characteristics, such as annual sediment loads, makes it very difficult t o detect changes within time spans that are useful for land managers or con ducive to adaptive management. (C) 2001 Elsevier Science B.V. All rights re served.