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Demographic and Health Survey 2009-10 - Timor-Leste Ministry of ...

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A.4 SAMPLING PROBABILITY AND SAMPLING WEIGHTS<br />

Because <strong>of</strong> the non-proportional allocation <strong>of</strong> the sample to the different districts <strong>and</strong> to their<br />

urban-rural areas, sampling weights will be required for any analysis using TLDHS <strong>2009</strong>-<strong>10</strong> data to<br />

ensure the actual representativeness <strong>of</strong> the sample at the national level as well as district level. Since<br />

the TLDHS <strong>2009</strong> sample is a two-stage stratified cluster sample, sampling weights were calculated<br />

based on sampling probabilities separately for each sampling stage <strong>and</strong> for each cluster. We use the<br />

following notations:<br />

P1hi: first-stage sampling probability <strong>of</strong> the i th cluster in stratum h<br />

P2hi: second -stage sampling probability within the i th cluster (households)<br />

Let ah be the number <strong>of</strong> clusters selected in stratum h, Mhi the number <strong>of</strong> households<br />

according to the sampling frame in the i th cluster, <strong>and</strong> ∑ M hi the total number <strong>of</strong> households in the<br />

stratum h. The probability <strong>of</strong> selecting the i th cluster in the TLDHS sample is calculated as follows:<br />

ah<br />

M<br />

∑ M<br />

Let b hi be the proportion <strong>of</strong> households in the selected segment compared to the total number<br />

<strong>of</strong> households in the EA i in stratum h if the EA is segmented, otherwiseb hi = 1.<br />

Then the probability<br />

<strong>of</strong> selecting cluster i in the sample is:<br />

P<br />

1hi<br />

hi<br />

hi<br />

ah<br />

M<br />

=<br />

∑ M<br />

Let g hi be the number <strong>of</strong> households selected in the cluster. The second stage’s selection<br />

probability for each household in the cluster is calculated as follows:<br />

hi<br />

hi<br />

ghi<br />

P 2 hi =<br />

M b<br />

The overall selection probability <strong>of</strong> each household in cluster i <strong>of</strong> stratum h is therefore the<br />

production <strong>of</strong> the selection probabilities:<br />

hi<br />

× b<br />

hi<br />

Phi = P1<br />

hi × P2<br />

hi<br />

The design weight for each household in cluster i <strong>of</strong> stratum h is the inverse <strong>of</strong> its selection<br />

probability:<br />

W = 1/<br />

P<br />

A spreadsheet containing all sampling parameters <strong>and</strong> selection probabilities was constructed<br />

to facilitate the calculation <strong>of</strong> sampling weights. Household sampling weights <strong>and</strong> the individual<br />

sampling weights were obtained by adjusting the above calculated design weight to compensate for<br />

household non-response <strong>and</strong> individual non-response, respectively. These weights were further<br />

normalized at the national level to achieve the number <strong>of</strong> un-weighted cases equal to the number <strong>of</strong><br />

weighted cases for both households <strong>and</strong> individuals at the national level. The normalized weights are<br />

valid for estimating means, proportions, rates <strong>and</strong> ratios, but not valid for estimation <strong>of</strong> totals. No<br />

special weights were calculated for data collected on children because there was not a child’s<br />

questionnaire. For child indicators tabulated at the household level, household weights should be<br />

used; for child indicators tabulated at the individual level, the child’s mother’s/guardian’s weight<br />

should be used.<br />

Sampling errors for selected indicators are calculated <strong>and</strong> presented in Appendix B.<br />

hi<br />

hi<br />

hi<br />

Appendix A | 257

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