# **3. Sampling Methodologies**

For each of the methods (satellite mapping, segmentation, grid squares, Qibla method, and random walk) and assignment mechanisms (random assignment, spatial clustering, and extreme spatial clustering), 10,000 simulated samples were drawn and relevant probability weights calculated. Each sample consisted of ten structures per PSU. For the cases in which the household sample was selected in two stages, two segments of five households were chosen within each PSU for segmentation, and two grid boxes of up to five households were randomly chosen in the grid square selection. This section provides further detail on the selection methods and describes the weight calculations necessary to achieve unbiased results.

# _3.1 Satellite mapping_

A full mapping of the PSU entails using satellite maps to identify the outline of each structure (see appendix). In this case, we used maps publically available on Google Earth and maps of the EA boundaries provided by the Somali Directorate of Statistics. From these maps, the structures inside each PSU can be assigned numbers (either by hand or digitally) and selected easily in the office with simple random sampling. The coordinates of the selected households can be loaded onto GPS devices to assist interviewers’ locating efforts.

This approach is the closest of the proposed study methods to the gold standard of a well‐implemented full household listing. The main differences are that in a field listing, enumerators can exclude ineligible structures, such as uninhabited and commercial buildings, and include information not available from satellite maps, such as the identification of individual units within multi‐household structures. In addition, whereas listing is always done just before the data collection, the satellite maps may be out of date, leading to under‐coverage of newly constructed units and/or selection of units that no longer exist. As noted in the previous section, the maps used for this paper were about one year old at the time of the initial analysis. The historical imagery from Google Earth indicates these maps are generally updated at least once a year, but this may vary substantially depending on the specific location and year. Selection from a satellite mapping therefore requires an additional set of field protocols for addressing and documenting the above issues.

The calculation of the probability of selection, and by extension the survey weight, is straight‐forward. � The probability is simply ~~,~~ where _n_ is the number of structures selected and _N_ is the total number of � structures, plus any necessary adjustment for multi‐household structures (for example, one unit from a three unit building) encountered in the field.

# _3.2 Segmenting_

Segmenting is a standard field procedure of subdividing large PSUs into smaller units, approximately equal sized in terms of number of households, for listing and selection purposes. The individual segments are

> estimating the true mean in the population, it should not affect the means when compared between methods.  First, as this bias is associated with a selected household’s decision to participate, it would impact all methods equally. Secondly, as non-response attenuates any differences, they would appear smaller in magnitude in the simulations than in the true population.  To address this, we ran a large number of simulations to generate narrow confidence intervals on the results.

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