Design-based versus model-based sampling strategies: Comment on R. J. Barnes' “bounding the required sample size for geologic site characterization”

Two fundamentally different sources of randomness exist on which design and inference in spatial sampling can be based: (a) variation that would occur on resampling the same spatial population with other sampling configurations generated by the same design, and (b) variation occurring on sampling other populations, hypothetically generated by the same spatial model, using the same sampling configuration. The former leads to the design-based approach, which uses classical sampling theory; the latter leads to the model-based approach and uses geostatistical theory. Failure to recognize these two sources of randomness causes misunderstanding about dependence of variables and the role of randomization in sampling, unwarranted narrowing down the choice of sampling strategies to those that are model-based, and abuse in simulation experiments. This is exemplified in Barnes' publication on the required sample size for geologic site characterization by nonparametric tolerance intervals. A basic design-based strategy like Simple Random Sampling is shown to require smaller sample sizes than the model-based strategy advocated by Barnes. In addition, Simple Random Sampling is completely robust against model errors and less complicated.