Evaluation of variance models for fractionator sampling of trees

We compared the performance of several models for predicting, from small samples, the precision of estimates of the total number of blossoms on fruit trees obtained using a three-stage fractionator, in which the sampling units were defined by the tree structure: (1) primary branches and stem (2) secondary branches and shoots and (3) flowering buds. The models considered were the semiempirical models of Cruz-Orive (1990, 2004) (CO), a random sample model (SR), a Poisson model (P), successive differences (D) and repeated systematic sampling (R). Procedures that relied upon a single sample and a model of the variance (SR, P, D) were not able to predict the estimator variance because the considered structures strongly violated model assumptions. The semiempirical CO model performed acceptably in some cases where model assumptions were violated to a moderate degree. The repeated systematic sampling procedure, which does not rely upon a model of the variance, usually provided very good predictions when the resampling terms were distributed appropriately across more than one sampling stage.