Effect of cluster sampling in biomass tables construction: linear regression models

Abstract

To construct tree biomass tables it is customary to select the sample trees by cluster sampling and then to apply the classical least squares regression techniques under the assumption of simple random sampling. A modified linear regression procedure is proposed for which the assumption of simple random sampling is no longer required. The procedure can be used when (i) the regression of a biomass component on tree characteristics other than biomass can be approximated reasonably well by a linear function and (ii) the number of sample clusters is sufficiently large. Applied to two large cluster samples of trees, where the cluster size is approximately equal to five trees, and compared with the classical linear regression approach, the modified procedure results in biomass tables which arc essentially the same. The confidence intervals, however, are quite different. The classical least squares regression method results in intervals which, on the average, are about 60% as large as those calculated by the modified procedure.