Survey Methodology
Coordination of spatially balanced samples

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by Anton Grafström and Alina MateiNote 1

  • Release date: December 20, 2018


Sample coordination seeks to create a probabilistic dependence between the selection of two or more samples drawn from the same population or from overlapping populations. Positive coordination increases the expected sample overlap, while negative coordination decreases it. There are numerous applications for sample coordination with varying objectives. A spatially balanced sample is a sample that is well-spread in some space. Forcing a spread within the selected samples is a general and very efficient variance reduction technique for the Horvitz-Thompson estimator. The local pivotal method and the spatially correlated Poisson sampling are two general schemes for achieving well-spread samples. We aim to introduce coordination for these sampling methods based on the concept of permanent random numbers. The goal is to coordinate such samples while preserving spatial balance. The proposed methods are motivated by examples from forestry, environmental studies, and official statistics.

Key Words:      Coordination; Local pivotal method; Spatially correlated Poisson sampling; Permanent random numbers; Unequal probability sampling designs; Transformed spatially correlated Poisson sampling.

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How to cite

Grafström, A., and Matei, A. (2018). Coordination of spatially balanced samples. Survey Methodology, Statistics Canada, Catalogue No. 12-001-X, Vol. 44, No. 2. Paper available at


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