Scale effects in survey estimates of proportions and quantiles of per unit area attributes

Quantiles and proportions in a sampling distribution of a per unit area attribute (Y) depend on the spatial support (area) of employed survey plots. This is a nuisance for managers, and policy developers; in particular when the underlying data have been collected with different spatial supports. Users of these statistics may wish to calibrate their estimates to a common scale of spatial support. The easiest way to do this is through scaling to a common plot size. We demonstrate a statistical method for upscaling. The method is illustrated in the context of a design-based forest inventory of a target attribute Y with a census of a co-located vector of auxiliary variables (X) correlated with Y. Two case studies from Norway and Switzerland confirmed significant and practically important scale effects in quantiles and proportions of above ground live tree biomass (Mg ha−1) and stem volume (m3 ha−1). Upscaling requires an estimate of the spatial autocorrelation of Y given X at the scale of the original spatial support. We present an expedient method to this end. Our method affords estimation of scaled quantiles and proportions and assures consistency of sampling distribution across scales.