Sampling Designs - Sampling Spatial Units for Agricultural Surveys - page 102

Chapter 6
Sampling Designs

6.1 Introduction

Sampling theory tells us that a design is uniquely defined by the list of all possible
samples that can be selected from a population U , and by the stochastic distribution
p ( s ) that assigns a probability of selection to each sample (see Sect. 1.2 ). The
number of possible different subsets of the population is very large, even if the size
is fixed. The result of the simple R function choose(40,10) ¼ 847660528 is
enough to understand the practical impossibility of drawing these samples.
Sampling units are almost always selected using a scheme that generates sam-
ples from p ( s ) using some pseudo-random number generators. These schemes are
used because of the large number of possible samples. They are also used so that we
can translate some operational requirement of the sampled units into the selection
routine, which may not be possible to describe using the probabilities on the set S .
The term sampling scheme refers to the collection of techniques or rules used to
select the sample. The composition of the sample is thus randomized according to
the probabilistic definition of the sampling scheme (Lehtonen and Pahkinen 2004 ).
When planning a specific design, the random selection procedure should satisfy
several requirements. It is not necessarily the most important requirement that the
sampling error should be as small as possible. Often, organizational matters such as
the availability of the frame or the cost of data collection may be important to the
sample selection. However, a well-organized survey is the result of a process that
has appropriately translated operational needs into correct methodological deci-
sions, which will help to draw reasonable samples. The concept that a sample
should be representative of the population resembling its characteristics is not
inexorably true. We could, for example, be interested in an oversample of some
portions of U such as the largest farms. Or we may wish to avoid observations from
some specific groups that would be selected with very low probability, or excluded
from the sample drawing process, as in cut-off sampling.