The calculation of the probabilities of _Source: Authors’ diagram based on PSU boundaries and_ selection is also straightforward: it is the _Google Earth images_ product of the probability of selection of the segment and the probability of selection of the household within the segment. The additional clustering introduced by this method, however, could decrease the precision of estimates due to the design effects. The magnitude of the decrease in precision would depend on the number of segments selected, the number of households selected per segment, and the degree of homogeneity within PSUs for the study variables. The impact would largest if all ten households were selected from the same segment, and decrease as more segments were selected. At the other extreme, if one household were selected from ten segments, segmentation would produce more precise estimates than simple random sampling as the segmentation prevents a chance geographic concentration of selected households. As a balance between efficiency and practicality, two segments and five households per segment were selected for the simulations.

# _3.3 Grid Squares_

To implement the grid method, a uniform grid of squares (or other uniform shape) is overlaid on the PSU map. Figure 1 shows an example using 50 x 50 meter squares for the Dharkinley PSU. The area of a grid square includes all of the area that lies both within the grid square and within the PSU boundaries. For example, in grid square 17 in figure 1, the majority of the structures inside the square would not be eligible for the survey, as they lay outside of the PSU boundaries. Only the structures which lie in the bottom left corner are both within the grid and PSU boundaries.

One or more squares can then be selected with simple random sampling from the set of all squares that overlap the selected PSU. Depending on the survey protocols, a structure may be defined as eligible if all or part of it lies within the grid space. The more common protocol, including the structure if the majority lies within the grid square, has the benefit of simplifying the weight calculations, but the risk of subjective decisions made by interviewers in the field about where the majority of the building lies, which could lead to some buildings having no chance of selection. Since the options for supervision and field re‐verification were limited in this survey, it was decided to consider the structure as eligible if any portion of the structure lay within the grid boundaries, to ensure that all units had a positive probability of selection.

To select a sample of households within the selected squares, a common approach would be for interviews to be conducted with all eligible respondents within the grid square. This could lead, however, to issues with verification as well as decreasing control over the final total sample size. Therefore the protocol used in Mogadishu had interviewers list all households within the selected squares and use the application on their smart phones to select a fixed number of households for the survey.

This variation of the grid method has the advantage that it requires less preparation time compared to mapping or segmenting. There are considerable drawbacks, however, in the ease of implementation and additional work to accurately calculate the selection probabilities. Since the grid squares do not follow visible landmarks, the boundaries must therefore be programmed into the GPS and identified by the interviewers. As it is unlikely that they will be able to walk straight along the boundary, additional training may be required to correctly identify eligible structures.

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