Sampling Designs - Sampling Spatial Units for Agricultural Surveys - page 136

farms, and/or with reference to land use codes; landscape, or other environmen-
tal parameters for other spatial units.
• The average time of permanence in the same stage, and the frequency of
transitions or certain events over a given time interval.
In rotating samples, the units to be observed on various survey occasions are
formed by replacing some statistical units with other randomly selected units. This
type of design is almost always used in surveys that have two purposes: to provide
estimates of the parameters of the population in different periods and their net
changes, and estimates of the dynamics of the observed phenomenon.
Thus, when planning a survey to provide data across time, we can choose
between repeated cross-sectional, rotating panel, and full panel designs. If the
data are to be used for longitudinal analyses, then we must use a panel design.
However, if the data are only to be used for an overall trend analyses, any design
can be used, provided that the sample is refreshed at each wave to represent new
entrants to the population (Kalton 2009 ).
When sampling spatial units in a closed population, the tuning obtained through
units rotation is only performed to calibrate n on the observed non-response rate. A
rotation of, for example, 20 % of the units per year is often introduced into the
sampling strategy to limit the cost of the field work, by reducing the amount of units
to be identified before the observation task. The organization and management of
interviewers and support tools such as maps or aerial photographs may also benefit
from an overlap with previous periods of the survey. The hypothesis underlying this
choice is that by keeping approximately 80 % of the units in the sample from 1 year
to the next, we greatly facilitate the identification and localization of the units and
also reduce the cost and time needed for data collection.
Random selection without replacement of the units is performed using the
permanent random numbers technique (PRNs, Ohlsson 1995 ).
The concept of coordination based on PRN was introduced in the 1970s.
Currently, most NSIs use variations of methods based on PRN sampling. Order
sampling was proposed by Ros´n( 1997 ), and is another approach that takes into
account the main idea of PRN.
The coordination of stratified samples is a more complex problem. This is
because over time units can change from one stratum to another. Several methods
for obtaining maximal or minimal coverage between samples drawn on different
occasions have already been developed (see Nedyalkova et al. 2008 for a review).
Practically, the PRN independently associate a pseudo -random number R k to
each unit k of the frame (of size N ). The vector of these realizations is then stored
together with the data for the units, to be re-used in future drawings. The stratified
random sample is then obtained by ordering the units (ascending or descending) by
stratum and random number, to obtain a random permutation of the units for each
stratum h. Then, the first (or last) n h are kept as the sample. This technique is
particularly simple to implement, and guarantees that every selection of contiguous
units from the ordered list constitutes a random sample of fixed size, which has first-
order inclusion probabilities equal to n h / N h .