1- Sample Design and Estimation
The sample of non-Qatari households (and small labour gatherings) was stratified by municipality and within each municipality the sample households were selected by a systematic sampling scheme after sorting the household serial numbers by zone and within zones by household size. The target sample size was allocated to the 10 municipalities of Qatar on the basis of the square-root allocation formula.
For the non-Qatari population living in large labour gatherings, sample selection was made directly at the individual level on the basis of a systematic sampling scheme in each municipality. The target sample size was allocated to the municipalities on the basis of the square-root allocation formula as in the case of the sample of non-Qatari households.
2- Design Weights
For the sake of clarity, a given municipality is designated by h and the following terminology is adopted to refer to the corresponding sample information:
Nh = Total number of non-Qatari households and small labor gatherings in municipality h.
Ph = Total number of persons in non-Qatari households and small labor gatherings in municipality h.
nh = Number of sample non-Qatari households and small labor gatherings in municipality h.
n′h = Number of responding units in sample of non-Qatari households and small labor gatherings in municipality h.
p′h = Number of responding persons in sample of non-Qatari households and small labor gatherings in municipality h.
1. The probability of selection of a sample non-Qatari household or small labor gathering in municipality h is given by:
Πh = nh / Nh
And the design weight is the inverse of the probability of selection, given by:
wh = Nh / nh
2. The probability of selection of a sample person in a non-Qatari large labor gathering in municipality h is given by:
Πh = ph / Ph
And the design weight is the inverse of the probability of selection, given by:
wh = Ph / ph
3. The probability of selection of a non-Qatari labour gathering depends on the size of the labour gathering. Larger labour gatherings have a higher probability of selection than smaller labour gatherings. Let mhj represent the size of labour gathering j in municipality h. Its probability of selection is given by:
Πh (labor gathering of size mhj) = 1 − combin(Mh − mhj, mh) / combin(Mh, mh)
Where combin(a, b) represents the combinatorial number of ways that b objects can be selected from a total of a objects,
combin(a, b) = a! / [b!(a − b)!]. As in other units, the design weight for labour gatherings is calculated as the inverse of the probability of selection. In practice, because of the large values of the entries, the combinatorial numbers are calculated using the Stirling approximation on the basis of average sizes of labour gatherings per zone and per municipality.
4. It should be observed that the probability of selection of a person in a non-Qatari household is equal to the probability of selection of the household in which he or she belongs. Therefore, the design weights for households and individuals are the same in the case of non-Qatari households. For non-Qatari labour gatherings, however, the probability of selection of individuals and that of labour gatherings are different, and as a result the corresponding design weights are also different.
3- Statistical Treatment for Unit Non-Response
The formula used for calculating the response weights in relation to the non-response rate is given below:
Response weight (Non-Qatari households) = 100 / (100 − non-response rate)
Where non-response rate = 100 × (nhk − n′hk) / nhk.
In the case of non-Qatari labour gatherings, weight adjustment for non-response was based on the assumption that non-respondent individuals in a zone are similar in terms of the survey characteristics with the responding individuals in that zone. No adjustments were made for non-response at the labour gathering level as the basic sampling unit was the individual rather than the labour gathering. The formula for response weight calculation of non-Qatari labour gathering population is given below:
Response weight (Non-Qatari labour gathering population) = 100 / (100 − non-response rate)
Where non-response rate = 100 × (phk − p′hk) / phk.
4- Consistency with Census Enumeration Results
The third stage in the construction of the weights is the use of auxiliary information to calibrate the sample-based estimates to the March 2004 census results based on complete counts of the non-Qatari population.
1. Non-Qatari Households
Census control weight (Male non-Qatari household members) = M′h / estMh
Where M′h is the March 2004 census count of the male non-Qatari household members in municipality h and the corresponding sample-based estimate is:
est Mh = ∑k (Nh/nh)(nhk/n′hk)m′hk
Where m′hk is the number of reported male non-Qatari household members in the sample from zone k in municipality h. The other terms (Nh, nh, nhk and n′hk) have been defined earlier.
The corresponding census control weights for women are given by:
Census control weight (Female non-Qatari household members) = F′h / estFh
Where F′h is the March 2004 census count of the female non-Qatari household members in municipality h and the corresponding sample-based estimate is:
est Fh = ∑k (Nh/nh)(nhk/n′hk)f′hk
Where f′hk is the number of reported female non-Qatari household members in the sample from zone k in municipality h.
2. Non-Qatari Compounds
Where M′h and F′h are, respectively, the March 2004 census count of the male and female populations in non-Qatari compounds in municipality h, and the corresponding sample-based estimates are:
est Mh = ∑k (Ph/ph)(phk/p′hk)m′hk
est Fh = ∑k (Ph/ph)(phk/p′hk)f′hk
Where m′hk and f′hk are the respective numbers of reported male and female persons in the sample of non-Qatari compounds in zone k in municipality h.
5- Final Weights
Final weight = Design weight × Response weight × Census control weight
