Sampling Designs - Sampling Spatial Units for Agricultural Surveys - page 109

3.4 3 4 11965.260 3247.188

1.5 1 5 8374.575 2911.359

2.5 2 5 4829.743 2256.235

3.5 3 5 4785.640 2235.957

6.3 Systematic Sampling

Systematic sampling has a long tradition in survey sampling (see Zhang 2008 for a
review). When applied to a list frame of individuals or families, it can be referred to
as the every rs- th rule . The main parameter of the method is rs , which is the number
of units between each unit selected from the sample, according to a given ordering
of the population. The randomization principle is typically retained by using a
random starting point and a fixed interval rs . This scheme is a widely used
technique in survey sampling because of its simplicity, particularly when the
units are selected with equal probability, but also with probabilities proportional
to an auxiliary size measure (see Sect. 6.4 ).
Systematic sampling is very practical in situations where a unique updated
version of the frame is not available in the central institute conducting the survey,
but is available in local or regional offices. Thus, the random sample cannot be
selected once for all interviewers. The surveyors define the selection rules to be
applied at a local level, which must obviously be very simple and should not
involve complex random number generations.
However, apart from its simple application, it can also be very efficient if the
researcher produces favorable stratification effects by listing the units. In other
words, much of its efficiency depends on the criteria used to sort the frame.
However, it can be very inefficient when the ordering of the population is based
on incorrect or inaccurate knowledge. A typical cautionary choice is to avoid any
gain or loss by randomly ordering the list prior to systematic selection.
Where the ordering of the units is plausibly uncorrelated with the survey variable
of interest, or contains at most a minor stratification effect, systematic sampling is
generally considered as a convenient substitute for SRS

“with little expectation of a gain in precision” (Cochran 1977 , p. 229).
Because all the second-order probabilities are equal to zero within each step rs ,
one main disadvantage is that there is no unbiased method for estimating the
sampling variance. Moreover, the ratio N / n is not typically an integer, so it is
often impossible to find a step rs that is suitable for finding exactly n sampling
units (for a solution to this problem in univariate populations, see S¨rndal
et al. 1992 , p. 76). This practical difficulty may become relevant when the selection
should be repeated in groups of homogeneous units of the population, or in spatial
frames where we need at least a pair ( r x , r y ) of step parameters (one for each
dimension).