Sample size requirements for the determination of changes in soil nutrient pools

In long-term field studies, the number of soil samples required to detect a specified change is often determined by using the standard error of a soil property from a pilot study. When a soil property is highly variable, estimates of its standard error will also be highly variable. Therefore, it is useful to have confidence limits for the standard error in sample size calculations. We explored the empirical distribution of the standard error for several soil properties (total carbon pools, exchangeable cation pools, and forest floor element pools) using data collected from a northern hardwood forest site in central New Hampshire. We used a bootstrapping routine to simulate data sets for sample sizes ranging from 6 to 60 soil pits and computed the mean, 95%, and 98% confidence limits for the percentage change detectable by a specified number of sample observations. Using the 95% confidence limit for standard error resulted in as much as a twofold increase in the sample size requirement compared with the average standard error. For normally distributed data, the bootstrap confidence limits of standard error agree with those computed analytically. In the presence of modest nonnormality in the data, however, the analytic confidence limits do not agree with the bootstrap limits. Since the bootstrap procedure is free of parametric assumptions, it is a useful tool for general application in soil science.