Sampling Designs - Sampling Spatial Units for Agricultural Surveys - page 131

this sampling strategy, the organization must have a major control on the timeliness
of each single activity of the master survey, because even a small delay can
compromise the performance of all the derived surveys.
Agricultural surveys, particularly when based on a spatial definition of the
statistical unit, integrate the information observed in the field with auxiliary infor-
mation (see Sect. 10.2 ) gained through remotely sensed data (see Chap. 4 ) , other
sources such as thematic maps (see Chap. 3 ), or previous surveys.
Auxiliary information is acquired in the first phase, and is usually associated
with a very large sample size. However, prohibitive costs may mean that the survey
may not necessarily cover the whole population. When dealing with a point frame,
this first-phase is also used as tool for taking a finite population sample over the
continuous surface of the study region, consisting of an infinite number of virtual
points that overlay a regular grid. Then, it is possible to select a point for each cell
according to systematic criteria. This selection can be aligned or randomized, to
avoid the typical problems that arise when using systematic samples (see Sect. 6.3 ).
A sampling frame is set up using the auxiliaries that are available for these points
(see Chap. 5 ).
Most spatial surveys treat points lying on systematic grids as if they were
random. This is acceptable for point estimates, but it is not for variance estimates,
which empirical evidence suggests are typically overestimated. Theoretically, the
converse is also possible. If one suspects a periodicity of some kind, it is essential
that it does not coincide with the periodic structure of the grid (Mandallaz 2008 ).
The second-phase detects the land use codes using direct observations for a
subsample of the first phase sample. We can only gather information regarding the
yield of a particular crop in the third stage, by selecting the subsample of the units in
the second-phase that are growing the crop under investigation. In current surveys,
these two phases are repeated two or three times per agrarian season to account for
the variation in the timings of different crops.
Methodologically, one of the most popular and reported reasons to use a two-
phase sample (sometimes called a double sample) is that the available frame does
not contain any covariate. In addition, it is a relatively cheap collection method that
will provide a set of auxiliaries denoted by X, that are possibly correlated with the
characteristics of interest, y (Fuller 2009 ). The information content of X is thus key
to a successful two-phase sampling strategy.
In other words, this scheme is typically used when it is very expensive to collect
data regarding y, but it is relatively inexpensive to collect data on X. For example,
when conducting agricultural surveys it is very difficult and expensive to travel to
remote areas and collect field observations. But aerial photographs are relatively
inexpensive, and the photo interpretation of land use should be strongly correlated
with appropriate ground truth information (Legg and Fuller 2009 ).
Denote s a to be the selected sample from the first-phase of sampling, a. Note that
the HT estimator (Eq. (1.22) of Sect. 1.2 ) cannot be used because we cannot always
calculate π k (S¨rndal et al. 1992 , p. 346). To determine π k , we require the proba-

bilities p a ( s a ) (which are typically known), and the π k | sa, , which we do not know

because they may depend on the outcome of the phase a sample. A natural