Alternative and complementary approaches to spatially balanced samples

The spatial distribution of a population represents an important tool in sampling designs that use the geographical coordinates of the units in the frame as auxiliary information. These data may represent a source of auxiliaries that can be helpful to design effective sampling strategies, which, assuming that the observed phenomenon is related with the spatial features of the population, could gather a considerable gain in their efficiency by a proper use of this particular information. We present and compare various methods to select spatially balanced samples. These selection algorithms are compared with the intuitive principle of partitioning the space into n strata and selecting only one unit per stratum. The fundamental interest is not only to evaluate the effectiveness of such different approaches, but also to understand if it is possible to combine them to obtain more efficient sampling designs. The performances of the spatially balanced designs are compared in terms of their root mean squared error using the simple random sampling without replacement as benchmark. An important result is that these complex designs provide better results than the simple principle of stratifying the study area. It also does not help so much to improve efficiencies even if it is combined with balancing on known totals of some auxiliary variables, such as the geographic coordinates