Sampling Designs - Sampling Spatial Units for Agricultural Surveys - page 103

What is really important is that we know as much about the structure of the
population as possible, and it is desirable that this structure is exploited by the
sampling scheme. It is clear that the selection algorithm determines the statistical
properties of the Horvitz-Thompson (HT) estimator, particularly its variance, which
is known as the sampling error. What is less clear is that it also has a substantial
impact on non-sampling errors such as the non-response rate and measurement errors.
In the remainder of this topic, for simplicity we will use the terms sampling
scheme and sampling design as synonymous, although it should be clear from the
discussion above that the two definitions are quite different.
The layout of this chapter is as follows. Sections 6.2 , 6.3 ,and 6.4 are devoted to the
basic selection procedures that are the foundations of every sample design. These
procedures are the simple random, systematic, and unequal probabilities sampling
methods. Most of the survey designs used in practice use these elementary procedures,
or are a combination. Section 6.5 discusses features of the stratified design, which is a
simple and very efficient way to introduce some population structures to the sample
design. In Sect. 6.6 we introduce the possibility of managing the hierarchical structure
of U using multistage samples, while in Sect. 6.7 we show how the timing of a
phenomenon, the data collection costs, and the need for data integration can be
considered using multiphase design. Section 6.8 is devoted to a more general coordi-
nation problem between samples and different periods of the same sample, to take
advantage of the longitudinal structure of a survey. The ranked set sampling, described
in Sect. 6.9 , is a particular way of exploiting auxiliary information at a design level.
Sections 6.10 and 6.11 present some designs for rare and skewed populations. Finally,
the last section contains some concluding remarks. The main R codes for the methods
in this chapter, with applications to simulated data, are also provided.

6.2 Simple Random Sampling

Simple random sampling (SRS) is widely used in practice. It is a basic design that
can be used when previous information on the population structure is not available,
and we do not have any reason to discriminate between statistical units. In fact, this
technique is based on the requirement that each sample has an equal probability of
selection. Thus, the resulting sample constitutes a fair representation of the popu-
lation (Lehtonen and Pahkinen 2004 ). SRS s importance comes from the irreplace-

able role that it plays in two key topics. It can be used as the benchmark in design-
effect comparisons when investigating complex designs. Furthermore, many
advanced sampling plans use SRS as a primary randomization method to select
aggregates of units, or units within aggregates.
The most common SRS method used in practice is simple random sampling
without replacement (SRSWOR) for fixed n . Other similar methods include
Bernoulli sampling or simple random sampling with replacement (SRSWR).
However, these selection criteria are not typically practical, so for simplicity, the
abbreviation SRS is used for SRSWOR in the remainder of this topic.

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