Agriculture Reference
In-Depth Information
all the units of an identifiable population. Following S¨rndal et al. (
1992
), the
sampling frame can be also defined as
“any material or device used to obtain observational access to the finite population of
interest”.
In practice, the sampling frame permits access to the individuals of the target
population that we wish to investigate. The frame also contains any auxiliary
information that can be used for some special sampling techniques. The sampling
frame should be complete and up-to-date; we typically assume that there are no
omissions or duplicates, and so the population frame coincides with the target
population.
Usually, a frame is expressed in terms of a computer data file. Generally, it has
an identifier
k
¼1,
,
N
, where
N
is the number of population units. As previously
mentioned, the frame may contain other information. More formally, all the
available
...
information for
the
k
-th unit
can be denoted as
a vector
x
k
¼
ð Þ
, where
q
are the available variables. In matrix notation,
this information can be described as
x
k
1
x
k
2
...
x
kq
0
1
1
x
11
x
12
...
x
1
q
@
A
2
x
21
x
22
...
x
2
q
...
...
...
...
...
:
ð
1
:
1
Þ
k
k
1
x
k
2
...
x
kq
...
...
...
...
...
N
N
1
x
N
2
...
x
Nq
In this topic, we generally indicate a matrix using a bold and uppercase letter, and a
vector using bold and lowercase.
Unfortunately, prohibitive costs mean that it is impossible in many practical
circumstances to construct a frame for the elementary units of the population under
investigation. In this situation, the frame is formed by a list of sets of elements of
the population. For example, consider a sample survey for studying trees in a forest.
Obviously, a complete list of units (trees) is not available. However, the frame can
be regarded as a list of areas (sets of trees) where the trees can be observed and
investigated. In this case, an area frame is a spatial reference frame that is composed
of areal units. Each population element belongs to an areal unit, and can be
determined by examining the unit. Areal units may cover differently sized areas
and contain different numbers of elements. These concepts will be extensively
In survey research, statistical units constitute the element of analysis. Therefore,
a population can be perceived of as an aggregate of all the units under review. There
is typically a target population (the real population), a frame population
(a population based upon a list of units that ought to be in the real population),
and a survey population (a segment of the frame population from which data are
available when the frame population is enumerated). Note that there are distinctions
between the target population, the frame population, and the survey population.
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