INDICADORES DE GESTIÓN COMUNES A LAS TRES CARRERAS I. Gestión de la Carrera
II. Formación Profesional 2.1 Demanda de admisión
The stratification of an area frame is generally based on the geo-referenced features that can be observed on the land, possibly by means of image analysis or photo-interpretation. In an agricultural area frame, typical definitions of strata can be “agricultural land > 60 percent”, “agricultural land between 30 and 60 percent”, etc. Additional strata may be defined for specific crops or crop groups that are usually stable on the land. For example, a stratum can be defined with conditions of the type “irrigated crops > 50 percent”, “permanent crops dominant” or “grassland mixed with cropland”. The range of conceivable strata labels is very wide. Therefore, if a division of the territory into geographic units is used as the basis for an MSF, the unit should be characterized by a set of variables, e.g. proportion of arable land, of irrigated land, permanent crops, grassland, etc. For each specific survey, statisticians must define a suitable stratification on the basis of the information available. When EAs are used as PSUs, a very efficient stratification can be defined on the basis of information derived from the most recent agricultural census. Each sampling unit must belong to one and only one stratum. Tests have been conducted on splitting segments with strata boundaries. A part of a segment would belong to stratum h and another part to stratum h’ (Gallego et al., 1994). Thus far, however, this approach has not yielded good results.
In practice, the information on the variables that characterize the frame units is likely to be far from perfect, but this does not mean that the stratification will be inefficient. If a land cover map is available and an area frame of segments is being constructed, it must be adapted if a stratification is to be built from it: First, the legend of the land cover map should be simplified, such that only the classes that are truly meaningful for the survey’s purposes are retained (e.g. rain-fed arable, irrigated arable, permanent crops, complex semi-agricultural landscape and non-agricultural). The strata boundaries should follow the geometry of the segments, in particular for segments with a regular (square) shape. Segments with physical boundaries can be delineated at a later stage, respecting the strata boundaries. For each segment, the area of each land cover class must be computed. In Figure 6.10, a square segment is overlaid on a land cover map. According to the map, the segment contains two land cover classes: forest and rain-fed arable land. In this example, the map and the background image show significant differences, partly due to the minimum mapping unit of the land cover map. For stratification purposes, the area of each class must be computed from the land cover map and reported in the attribute table of the list of segments. This table will enable analysts to define the stratification for each specific survey.
The situation is slightly different for point sampling: each point belongs to a land cover class and the stratification can be defined directly, by simplifying the nomenclature of the land cover map. There can be strata such as “rice”, “other irrigated arable land”, “rain-fed arable land”, “permanent crops”, “heterogeneous agricultural areas”, etc.
6.3.2. Single- and multi-stage sampling
A two-stage point sample survey can be seen as a segment survey with an incomplete observation of segments. In the first stage, a sample of area units (PSUs) is selected. In the second stage, a sample of points is drawn in each PSU selected in the first stage. In this case, the PSUs will be segments, but small administrative units (EAs) can be also used. A range of techniques may be applied for the second sampling stage, including stratified random sampling and different types of (possibly stratified) systematic sampling.
As noted above, the term “PSU” is not always linked to a proper two-stage sampling scheme. In particular, the segment sampling approach used by USDA-NASS is an improper two-stage sampling process, because only one SSU is selected in each PSU. In this case, the PSUs are a tool to reduce the amount of GIS work, and the two-stage sampling formulas for variance estimation need not be used.
6.3.3. Multi-phase sampling
The idea of multi-phase (most often, two-phase sampling) sampling is linked with the principle of the MSF. In two-phase sampling, a large sample is selected in the first phase; this first-phase sample or pre-sample is generally stratified by means of a procedure that is more statistically efficient than a stratification system applied to the full area frame. If this happens, and the first-phase sample is sufficiently large, this large sample can be a good master sample, or a basis for one.
Two-phase sampling is particularly useful for non-clustered point sampling. Typical examples are the Italian AGRIT survey (since 2002) and the Eurostat LUCAS survey (since 2006). The method has also become operational in Haiti, and pilot tests are being conducted in several sub-Saharan countries. In both AGRIT and LUCAS, the first-phase sample is a systematic grid over the targeted region’s entire area. The grid has a 500 m step in AGRIT and a 2 km step in LUCAS (Figure 6.6). The points in the grid are photo-interpreted on aerial ortho-photos or VHR satellite images with a simplified nomenclature, such as “arable land”, “permanent crops”, “pastures” and “non-agricultural”.
FIGURE 6.10
Photo-interpretation of a point is usually more accurate than polygon photo-interpretation in producing a land cover map, because the photo-interpreters focus their attention upon a single point. The better quality of photo- interpretation largely makes up for the loss of efficiency deriving from the incompleteness of the stratification (only the first-phase sample of points is stratified). The first-phase sample (which usually comprises a very large number of points) is subsampled in the second phase with a rate that depends on the strata, such that most of the final sample is concentrated on the strata with the highest priority.
6.3.4. Systematic sampling
Systematic sampling is often applied in list frames: the elements of the frame are sorted in accordance with a given criterion and the sample contains the elements i, i+k, i+2k, etc., where i is random and the step k is adjusted to obtain the targeted sample size (see Chapter 3 of this Handbook). The efficiency of systematic sampling depends on the degree of auto-correlation between neighbouring elements: it avoids elements that are excessively close to each other and the corresponding redundancy of information, measured by auto-correlation.
In area frames of segments with physical boundaries, systematic sampling is sometimes applied by ordering PSUs in a serpentine arrangement; however, this does not necessarily avoid neighbouring elements from being present in the sample. Systematic sampling in an area frame uses jumps of amplitude kx and ky along both X and Y axes (possibly
with the same horizontal amplitude kx=ky), and is a better guarantee of homogeneous geographic distribution.
The main disadvantage of systematic sampling is that there is no unbiased estimator of the variance; however, the ensuing practical implications are limited. The usual formulas for random sampling overestimate the variance under systematic sampling; however, alternative formulas based on local variances have been proposed to substantially reduce the bias (Wolter, 1984). A more significant drawback of straightforward systematic sampling is the difficulty of revising the sample size to the available budget, without rerunning the entire process (Stehman, 2009). Systematic sampling with multiple replicates maintains good spatial distribution and subsequent standard error reduction, and is flexible enough to accommodate sample size changes and the unbiased estimation of sampling errors (Gallego and Delincé, 2010).
When the results of a sampling survey are politically sensitive and there is a risk that stakeholders may not accept them, wishing rather to verify each step, systematic sampling has the advantage of being more easily traceable. In random sampling, it is more difficult to prove that the sample is truly the outcome of the first attempt at extracting random numbers.