# Canadian Forest Service Publications

Scale effects in survey estimates of proportions and quantiles of per unit area attributes. 2016. Magnussen, S.; Mandallaz, D.; Lanz, A.; Ginzler, C.; Næsset, E.; Gobakken, T. Forest Ecology and Management 364, 122–129.

**Year:** 2016

**Issued by:**
Pacific Forestry Centre

**Catalog ID:** 36931

**Language:** English

**Availability:** PDF (request by e-mail)

Available from the Journal's Web site. †

DOI: 10.1016/j.foreco.2016.01.013

† This site may require a fee

## Abstract

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 (m^{3} 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.

## Plain Language Summary

Forest resource statistics depends on the number and size of field plots. With two examples from actual forest inventories we demonstrate the effect of changing the field plot size on estimates of: i) the proportion of forest area with less than a user defined threshold value of a variable of interest (e.g. biomass); and ii) the value of a variable of interest that is not exceeded in a user specified percent of the forest area. We also demonstrate how a nonlinear transformation of an observed variable introduces a scale dependent shift in the sample mean. Because nonlinear transformation are often used in process modelling of forest ecosystem services, the scale effect in a mean is a nuisance and complicates comparison of results obtained with different plot-sizes.