Sampling Designs - Sampling Spatial Units for Agricultural Surveys - page 141

6.11 Cut-Off Sampling

Cut-off sampling is commonly used by NSIs to select samples, but it is not easy to
give a precise and widely accepted definition. A distinctive feature is that we know
part of a target population that must be excluded in advance.
In the basic formulation (S¨rndal et al. 1992 , pp. 531-533) there is a set of
thresholds on one or more auxiliary variables, and the units with these variables
under thresholds are always discarded. In other words, their π k are set to zero. In

agricultural surveys, these thresholds typically regard the size of a farm or house-
hold measured in terms of arable land, or the percentage of produce that is for
market or self-consumption.
Some additional constraints such as the elevation and slope can be imposed
when sampling spatial units. In fact, at least in Europe, arable land can be observed
by requiring that the selected sample units are below 1,500 m, or an irrigated crop
can be observed by requiring that the slope is less than 30 %. Moreover, census data
may tell us that 95 % of the production of a given crop is concentrated in only two
or three regions of the country. In such a case, we may want to focus the sample in
these regions by setting the probability of selecting units outside equal to zero.
In general, the population is partitioned into two or three strata, and the units in
each stratum are treated differently. The most general definition of cut-off sampling
refers to this framework, with the three strata of the population composed of units
that are completely enumerated, sampled, and discarded. This type of stratification
is particularly appropriate for farms or households, as their distribution is mostly
skewed (Benedetti and Piersimoni 2012 ). When the distribution of the selection
variable is concentrated in few large units, cut-off sampling usually provides a
sample with a rather small size but a high degree of coverage. If the objective of the
survey is the estimate of the population total, a considerable percentage of obser-
vations will have a negligible contribution on the total; however, it is essentially
mandatory that we include the largest units of the population in the sample.
However, it is well known that cut-off sampling produces biased estimators (see,
for example, S¨rndal et al. 1992 , p. 531). Therefore, the error is typically measured
using the MSE, and cut-off sampling may be the preferred choice when the variance
reduction more than counterbalances the introduction of a small bias (Benedetti
et al. 2010 ).
From a methodological point of view, the goal is to optimally partition the
population into three sets: a take-all stratum whose units are surveyed entirely
( U C ), a take-some stratum from which an SRS is drawn ( U S ), and a take-nothing
stratum whose units are discarded ( U E ). The population size is denoted by N , the
sizes of U C and U E are denoted respectively by N C and N E , and the size N S of the
take-some stratum is given by N S ¼ N - N C - N E .

Roughly speaking, the part of the population that will be excluded is decided in
advance (for example, farms with less than 1 ha of arable land). This strategy is so
commonly used in business surveys (even in the agricultural sector) that its use is