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A simple random sample in an area frame usually gives a number of pairs of elements that are close to each other. These elements give redundant information since there is usually a high spatial autocorrelation at short distances. The efficiency of sampling is generally improved if we impose that the distance between two elements of the sample cannot be less than a certain threshold. However applying this restriction can introduce a significant perturbation of the sampling probability. Elements near the borders of the region are more likely to be selected. In the case of aligned sampling by repetition of a pattern in a square block, a distance threshold does not modify the marginal probability of each element of the population, although crossed probabilities are slightly changed.

SAMPLING SEGMENTS IN AN AREA FRAME WITH A DISTANCE THRESHOLD