Determining minimum sample size for the conditioned Latin hypercube sampling algorithm

In digital soil mapping (DSM), a fundamental assumption is that the spatial variability of the target variable can be explained by the predictors or environmental covariates. Strategies to adequately sample the predictors have been well documented, with the conditioned Latin Hypercube Sampling (cHLS) algorithm receiving the most attention in the DSM community. Despite advances in sampling design, a critical gap remains in determining the number of samples required for a DSM project. We propose a simple workflow and function coded in R language, to determine the minimum sample size for the cLHS algorithm based on histograms of the predictor variables using the Freedman-Diaconis rule for determining optimal bin width. Data pre-processing was included to correct for multimodal and non-normally distributed data, since these can affect sample size determination from the histogram. Based on a user-selected confidence interval (CI) for the sample plan, the density of the histogram bins at the upper and lower bounds of the CI are used as a scaling factor to then determine minimum sample size. The technique is applied to a field-scale set of environmental covariates for a well sampled agricultural study site near Guelph, Ontario, Canada, and tested across a range of CIs. The results showed increasing minimum sample size with an increase in the CI selected. Minimum sample size increased from 44 to 83 samples when the CI increased from 50% to 95%, then increased exponentially to 194 samples for the 99% CI. The technique provided an estimate of minimum sample size that can then be used as an input to the cLHS algorithm.