A Technical Note on PPS ~ling
Applica.tion to Fruit and Nuts
FJ:.ederic A. Vogel
Research and.Development Branch
Standards and Research Division
1. Basic Theory
One of the first
problems encountered whendesigning a sample is to
determine what criterion
to use as a basis for selecting
the 'sample units.
For example, should the sample units be selected with equal probabilities,
or with unequal probabilities
based on somemeasure of size? A typical
problem is encountered whendeciding howto obtain a sample of limbs in a
or nut tree for the purpose of estimating the total numberof fruit
nuts in the tree.
The production per tree is one of the most important com-
ponents in a forecasting model designed to estimate total production.
A numberof research studies have been conducted to determine the most
on which to base the sample selection.
The limb cross-
sectional area (CSA.) has been found to showa good correlation with the number
on the limb. The CSA. is currently used in several operatio~
as a measure of size for limb selection.
The "randompath" PPSmethod of limb selection as described by Jessen
is conunonlyused. This method is primarily used whenobtaini~
a sample of
only one limb per tree.
However,when the sample design makes it necessary ~o
obtain more than one sampling unit per tree,
is not clear howthe I sample
should 'Qedrawn, and what form the estimator should take.
In recent years, a large numberof selection procedures and estimators
have been proposed for sampling with unequal probabilities
when the sample size is greater
tnan one. These were reviewed with the intention
of finding one tpat was both efficient
for estimating the number
or nuts in a tree.
The following paragraphS outline
the 1>S.sictheory ••
then an estimator
It shouJ.dbe stressed at this