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Several European countries (Portugal, Spain, Greece, Rumania, and the Czech Republic) make crop surveys on area frame with an aligned systematic sampling of squared segments. So far crop area estimates are obtained with standard formulae for random sampling, without using the spatial structure of the sample. This is in general conservative, the estimated standard error is larger than the error actually made. Taking as clusters the set of segments with the same relative position in a block, gives often lower but very unstable variances. A more stable variance estimate is computed by repeated random permutations of the sample segments in each block before building up the clusters. There is most often a moderate variance reduction when no stratification has been performed. If the sample is stratified and the cluster estimator is applied in each stratum, the variances seem to be less unstable. In this case permutations in each block seem not to be very useful.

STRATIFICATION AND CLUSTER ESTIMATOR ON AN AREA FRAME BY SQUARED SEGMENTS WITH AN ALIGNED SAMPLE