Fieldworker 3.... Walking in their designated direction away from the SSP, they will select the fifth household for their first interview, counting houses on both the right and the left (and starting with those on the right if they are opposite each other). Once they leave their first interview, they will continue on in the same direction, and select the tenth household (i.e., counting off an interval of ten more households), again counting houses on both the right and the left. If the settlement comes to an end and there are no more houses, the Fieldworker should turn at right angles to the right and keep walking, continuing to count until finding the tenth dwelling” (Afrobarometer, pg. 35).

To simulate the random walk in the Mogadishu context, we replicate the Afrobarometer protocols to the extent possible. First we selected a random starting point (since it is not possible to identify landmarks with the level of detail available on the maps, we simply use a random point as the path start). To simulate the direction of the sun, a random angle is chosen and the direction of the interviewer’s path assigned at 90 degree intervals. For example, if 13 degrees from due north was selected, then the four paths would be at 13 degrees, 103 degrees, 193 degrees, and 283 degrees. From these lines, it was assumed that every dwelling within five meters on either side of the direction of walking was within the interviewer’s line of sight. These dwellings were sequentially numbered and every fifth dwelling selected. If the interviewer reached the PSU boundary before selecting the requisite number of households, the path made a 90 degree turn and continued. If each of the four interviewers selected three households, the total cluster size would be twelve. In order to ensure comparability with the other methods, each of which aimed to select ten households, we dropped the last two selected households.<sup>4</sup>

**4. Results**

# _4.1 Simulations_

For each of the sampling methods discussed above and the three different methods of allocating consumption values to households (random, some spatial clustering, extreme clustering), we simulated 10,000 samples and calculated the mean for each one. We report in table A2 in the appendix the mean, standard deviation,<sup>5</sup> 5<sup>th</sup> percentile, and 95<sup>th</sup> percentile of the distribution across all 10,000 samples and evaluate the different sampling approaches in terms of their bias and variance. If a sampling method is unbiased, the expected value of the sample means should be 40, by design the true mean consumption in each simulated PSU.

While generally it was possible to implement all of the methods in our simulations, there were notable challenges with three of the designs. In simulating the Qibla method, certain selected points did not lead to a selection within the EA. The impact was largely negligible in Heliwa or Hodon, where only 0.4 percent and 1.4 percent, respectively, of the total area led to no selection, but in Dharkinley, the smallest and most regular of the PSUs tested, 13 percent of the area led to no selection within the PSU, substantially decreasing the efficiency of that method. Then in the implementation the grid selection method, there was little control over the number of households in each grid square. In some cases, grid squares were

> 4 The analogous action in the field would be for the supervisor to rotate the additional interviews between interviewers to assure an even workload, though most likely in the design stage the cluster size would have been set to be evenly divisible among interviewers.

> 5 The standard deviation of the distribution is the standard error of the estimate of the mean.

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