Sample size estimation for achieving the desired uncertainty for estimates of tree fine root trait parameters

Abstract

This study investigates efficient strategies for fine tree root sampling, in terms of estimating root trait parameters with desired confidence intervals for least effort and cost. Sampling tree roots is difficult and costly with high variation among samples and wide confidence intervals for parameter estimates. Efficient strategies for fine tree root sampling will estimate root trait parameters with the desired confidence interval for least effort and cost. We compared alternative strategies to sample and estimate fine root surface area density; (1) collecting samples at intervals of 10 cm to a depth of 150 cm for entire tree root systems versus (2) independently taking samples from different randomly-selected 10-cm depth intervals around different trees. We also quantified the pilot sample size needed to reliably estimate the number of samples that would achieve the desired confidence interval. Efficiency of sampling entire tree root systems versus independent samples depended on the structure of the sample data. Pilot sample sizes > 5 per 10-cm soil depth can give reliable estimates of sample sizes required to achieve a 95% confidence interval of ± 10% of the sample mean. The statistical strategies in this paper are not particularly novel or difficult, but are seldom applied to root studies. We contend that they should be used, both to guide efficiency in sampling design and also to assess how realistic it is to expect that estimated sample means will be reliable, in the sense of having confidence intervals of the required width.