Statistical assessment of any monitoring scheme should always take place ahead of its implementation, and formal power calculations play an important role in such assessments. The power calculations can either be used to help find a design with a stated probability of detecting a given trend or difference in trends at some level of significance, or they can be used to provide information about the magnitude of trend or difference in trends which is likely to be detected by a proposed monitoring scheme. In either case, the power calculations require estimates of variances or variance components. This paper describes a case study in which statistical powers are compared for two competing models for random variation over years within sites: a random regression coefficient model and a first order autocorrelated error model. The response variables we present results for are unconstrained indices of butterfly abundance and constrained indices of plant species composition. The results indicate the effect of the different assumptions about random variation, in both the short and the long term. Copyright © 2011 John Wiley & Sons, Ltd.