Errors in estimating total root length by sub-samples method

A new method has been proposed to estimate the total length in a sample, and it assumes that roots are cylinders with a given bulk density. The technique is based on the measurement of the length and diameter of small pieces of roots, and on the measurement of the bulk density of root sub-samples. An exact formulation is presented of the error distribution in estimating total root length. This leads to a simple formula which relates directly the variance of the root length estimates to both the number of roots used in estimating the root characteristics, and the number of sub-samples used in estimating the mean bulk density of the samples. This enables analyses of experimental designs with respect to sample size and accuracy.