Essential Statistical Concepts, Definitions, and Terminology - Sampling Spatial Units for Agricultural Surveys - page 3

Sample survey inference is historically regarded using a finite population
approach, which infers certain parameter functions using the N variable values
associated with N units. A sample of n units, say s , is selected from the N units using
a specified stochastic procedure (the sample design). The parameters are functions
of the observations from the N individuals in the population. When inferring from a
finite population, the characteristics are considered to be non-random. In this case,
the aim of the survey is to provide information about some unknown population
characteristics or parameters. In other words, the only source of uncertainty is
represented by the probability of the population units belonging to the sample.
Sampling from finite populations leads to design-based inference.
However, in scientific applications, interest is sometimes focused on the gener-
ation of the population variables. To address this issue, we can consider that the
N population values are generated using a stochastic mechanism called a
superpopulation model. It characterizes the relationships between the variables of
different units of the population. Such a model enables us to make inferences about
population characteristics using “on sample” measurements. In practice, we use the
model to predict values for non-sampled units. Superpopulation modeling leads to
model-based inference.
We discuss the finite population approach to sampling in Sect. 1.2 , and the
superpopulation approach in Sect. 1.3 . Note that this topic is mainly concerned with
the sampling of geographically distributed data. For this reason, we discuss the
main statistical models for spatial data in Sect. 1.4 , as a necessary prerequisite to
spatial sampling methods. Finally, the last section concludes the chapter, and
outline the remainder of the topic. The R codes for the main formulas are described
in the narrative. See Zuur et al. ( 2009 ) for an introduction to R .
1.2 Sampling from Finite Populations
Another possible taxonomy of sampling is based on the techniques for selecting the
units. Methods can be classified as probability or non-probability sampling .In
probability sampling, we assume that each member of the population has a non-zero
chance of being selected. A probability sampling method uses some form of
random selection . Probability methods include simple random sampling, system-
atic sampling, and stratified sampling. In non-probability sampling, the units of the
population are selected using some subjective or ad-hoc procedures. These include
convenience sampling, judgment sampling, and quota sampling (Smith 1983 ). The
main advantages of probability sampling are that we can compute the sampling
error and reduce the bias caused by the subjective choices of a researcher. Sampling
error is due to only having observations from a subset of the population. It occurs
when we use samples to make inferences about the populations from which they are
drawn (S¨rndal et al. 1992 ).
In surveys that use a finite population approach, the observation of individual
population units is obtained using a sampling frame. The sampling frame is a list of