Coordination, combination and extension of balanced samples

The cube method allows the selection of balanced samples on several auxiliary variables with equal or unequal inclusion probabilities. Practical implementation of the cube method has raised questions concerning the selection of a multi-phase balanced sampling design, the rebalancing of an unbalanced sampling design by completing it with another sample, the selection of a balanced sample from an unbalanced sample and the coordination of balanced samples. This paper provides a complete solution of all these problems. Copyright 2004, Oxford University Press.