Estimating Soil Parameters and Sample Size by Bootstrapping

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Abstract
Collecting large numbers of soil samples (observations) to estimate parameters of certain soil properties is not always feasible, especially for undisturbed soil samples. If the number of soil samples is small, however, the usefulness of classical statistics is often limited and an alternative procedure is required to determine statistics of interest. A recently developed, computer‐intensive, statistical procedure; bootstrapping, is discussed for two bulk density applications for which relatively small numbers of observations were obtained. Bulk density was determined at 16 depths along 1.2‐m long soil cores taken at each of 60 locations in a 50‐ by 100‐m cultivated field (Norfolk sandy loam, Typic Paleudults). Initially, 16 locations were sampled. At a later date, the additional 44 locations were sampled at similar soil‐water conditions. For each core, bulk density was determined at 0.20‐, 0.40‐, 0.60‐, 0.80‐, and 1.00‐m depths by a paraffin technique and at 0.14‐, 0.26‐, 0.34‐, 0.46‐, 0.54‐, 0.66‐, 0.74‐, 0.86‐, 0.94‐, 1.06‐, and 1.14‐m depths by a direct method. Semivariograms, determined for each depth, generally showed no evidence of spatial interdependence between locations. Additional statistical tests indicated that the samples for the two dates came from different populations. Bootstrapping was used to determine confidence intervals for the population mean, variance, and range by sampling date without a priori assumptions as to the distribution of bulk density in the population. Bootstrapping was further used to develop a general method for determining the minimum sample size (minimum number of observations) that can be used to estimate the population mean with a selected degree of precision and level of confidence. Application of the bootstrap method indicated not only differences in bulk density on the two sampling dates but also differences in the precision of the bulk density measurement techniques.

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