Cluster size and number of clusters

167 ANNEX IV SAMPLE DESIGN AND IMPLEMENTATION

IV.7 Sample design implementation

Two major issues impeded the implementation of the sampling design during the ieldwork period. One was the security situation in parts of the country, which halfway the survey led to the introduction of the reserve sample. In total 133 clusters 6.3 percent of the original 2,100 clusters were thus replaced with ones from other districts. In addition, 17 clusters, representing 170 households, were not implemented and not replaced. Figure 1.1 in chapter 2 shows in which districts the survey was implemented according to the sample design, and in which districts fewer or no data collection took place. A second interference with the sampling design concerned delays in the ieldwork due to administrative, logistic and technical issues. This had the following implications: • The ieldwork was extended from 12 to 16 months in order to capture the full sample. • Information for spring and summer time was collected in two different years 2011 and 2012 • The Kuchi sample was implemented in winter 2011-12 and summer 2012 instead of summer 2011 and winter 2011-12. • There was especially an underrepresentation of coverage during the autumn season. Table IV.2 presents the number of households interviewed by season and year. In total 20,828 households were covered, 172 0.8 percent short of the targeted sample. Table IV.2 Interviewed households, by year, and by season Shamsi calendar Season Year Total 1390 1391 Spring 1,671 4,866 6,537 Summer 3,289 4,149 7,438 Autumn 2,753 2,753 Winter 4,100 4,100 Total 11,813 9,015 20,828 Non-response within clusters was very limited. Only in 797 3.8 percent of the scheduled interviews in the 2,099 accessed EAs households were not available or refused or were unable to participate. In 779 of these cases households were replaced by reserve households listed in the cluster reserve list, leaving 18 households unaccounted for 0.09 percent.

IV.8 Calculation of sampling weights and post-stratiication

By design, the sample observations in the sample are self-weighted. An implication of this is that the expansion factor for all observations within a speciic stratum is simply the ratio of the number of households in a stratum divided by the number of sample observations from each stratum. This applies to the provincial strata as well as to the Kuchi stratum. For the purpose of calculating the sampling weights, scaling factors were constructed based on the number of households in Afghanistan. The estimated number of households was derived from the CSO population projections by province for January 2012. For the settled population, the provincial population was divided by the average household size in the NRVA 2011 sample of each province to obtain the number of households in the middle of the survey period. This ratio is the scaling factor Whsq that expands the sample of households to the total population of households and relects the product of the probabilities of selection for the Primary Sampling Unit PSU and the Ultimate Sampling Unit USU: Whsq = [probPSU probUSU] where h identiies the household, s identiies the stratum, and q identiies the calendar quarter. 168 ANNEX IV SAMPLE DESIGN AND IMPLEMENTATION Because the unweighed sample allocation was not uniform across seasons, uncorrected annual estimates would place relatively larger weights on those seasons which had a large sample spring and summer, thereby distorting the representativeness of national results. Because the sample was stratiied by season, and imposing the assumption that the level of seasonal, international migration is negligible, the weighted distribution can be smoothed out to ensure that the estimated population size by quarter is the same. That is to say, the sample-based estimate of the population of Afghanistan is the same in the summer as it is in the winter. This adjustment is implemented as: Whsq = [probPSU probUSU] [0.25 POPs, 2012 ] ∑hsq HHSIZEhsq where POP is the CSO estimate for the settled population for January 2012 25,500,100. This population is divided by four to uniformly allocate the population to each quarter of the year assuming away seasonal international migration. The denominator term HHSIZEhsq is the size of household h in stratum s sampled in quarter q. The denominator gives the total number of sampled, settled individuals in each stratum by quarter. The adjustment term in the numerator gives the population of individuals for each stratum by quarter as estimated by CSO of the settled population. In order to obtain an expansion factor for the count of individuals the following calculation was made: whsq = Whsq HHSIZEhsq Whsq and whsq are included in the NRVA 2011-12 dataset as sampling weights to produce survey results for the total populations of households and individuals.