Power analysis and practical strategies for environmental monitoring

What sample size n is needed to have 1 - beta chance of detecting a magnitude delta response to pollution impact? A design where the same sites are sampled both before and after impact is more efficient than a design where sites are reallocated for the after-impact sampling. Taylor's Power Law can be used to estimate the n necessary to achieve specified power for a wide range of variance-mean relationships. Solutions can easily be obtained where the error coefficient of variation and the percentage change due to impact are of interest rather than the error standard deviation and absolute change. Estimation of the n necessary to detect a hypothesized multivariate response can easily be done. When p response variables are uncorrelated and all respond equally to impact, the required n is approximately the same as for a univariate test using one of the variables. If only one of the p variables responds, n is approximately p times that number. However, if the variables are correlated and the vector of response differs from the natural variation, then the required sample size is smaller. In this circumstance the multivariate test can be very powerful.