Sample Size and Sample Allocation - Sampling Spatial Units for Agricultural Surveys - page 214

Conclusions
In this chapter, we have described the main tools for answering the key
question “how many sampling units should be selected?” The fundamental
dilemma is that we should save resources while simultaneously gaining as
much efficiency as possible, or at least respect a fixed efficiency threshold.
These methods are generally derived from an arithmetic inversion of the HT
estimator variances, or are formalized within an optimization framework.
However, it is important to remember the inherent uncertainties in the
problem, which are a result of the unknown parameters of the population
used in the sample size estimation. For this reason, the solutions should be
considered a support device for the analyst, and experiences from past studies
or different data sources have an incomparable impact on the probability of
the success of the survey.
The improvements discussed in Sect. 8.5 can help, using models to
introduce external data or some prior knowledge into the sample design.
This additional flexibility is subjective, which often implies a loss of
robustness.
Note that the problem of total nonresponse has not been discussed in this
chapter, because it requires ad hoc solutions that depend on the nonresponse
mechanism that we assume for the population. For example, we may suppose
that there is a constant response rate within each stratum, leading to a
stratified two-phase sampling (see Chap. 6 ) . In these cases, the operational
and most widely used empirical solution for compensating for lost units is to
oversize the sample at a rate proportional to the inverse of the expected
nonresponse rate. In this way, assuming that a reliable estimate of the
nonresponse rate is available, the only negative effect might then be some
increase in the administrative burden and data collection costs (S¨rndal and
Lundstr¨m 2005 ).
Complex nonlinear programming solutions have been proposed so that we
can specify the constraints, not only for the entire survey, but also for an
efficient domain estimation (Choudhry et al. 2012 ). In this case, difficulties
may arise due to conflicts that may occur in constraints relevant to several
variables, which may regard different hierarchical levels of data aggregation
such as regions, counties, or municipalities. We should also consider that any
variation in the adopted estimation procedure or sample selection criterion
require further substantial changes to the proposed solutions. This can be very
challenging from a methodological point of view.
Considering that the most used strata codes for stratified sampling are
relative to an administrative or geographical nomenclature, it is worth noting
that sample allocation can be even more critical to fieldwork organization
than to the statistical efficiency of the estimates. Distributing the available
resources across a country, managing the interviewers, and handling the
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