Support, shape and number of replicate samples for tree foliage analysis.

Many fundamental features of a sampling program are determined by the heterogeneity of the object under study and the settings for the error (alpha), the power (beta), the effect size (ES), the number of replicate samples, and sample support, which is a feature that is often overlooked. The number of replicates, alpha, beta, ES, and sample support are interconnected. The effect of the sample support and its shape on the required number of replicate samples was investigated by means of a resampling method. The method was applied to a simulated distribution of Cd in the crown of a Salix fragilis L. tree. Increasing the dimensions of the sample support results in a decrease in the variance of the element concentration under study. Analysis of the variance is often the foundation of statistical tests, therefore, valid statistical testing requires the use of a fixed sample support during the experiment. This requirement might be difficult to meet in time-series analyses and long-term monitoring programs. Sample supports have their largest dimension in the direction with the largest heterogeneity, i.e. the direction representing the crown height, and this will give more accurate results than supports with other shapes. Taking the relationships between the sample support and the variance of the element concentrations in tree crowns into account provides guidelines for sampling efficiency in terms of precision and costs. In terms of time, the optimal support to test whether the average Cd concentration of the crown exceeds a threshold value is 0.405 m3 (alpha = 0.05, beta = 0.20, ES = 1.0 mg kg(-1) dry mass). The average weight of this support is 23 g dry mass, and 11 replicate samples need to be taken. It should be noted that in this case the optimal support applies to Cd under conditions similar to those of the simulation, but not necessarily all the examinations for this tree species, element, and hypothesis test.