4 Arab Jerusalem Sample Design
The sample design for Arab Jerusalem (AJ) is a stratified three stage design
similar to that of the West Bank, except for the omittance of the subselection
of cells. In order to keep the mathematical notations unchanged, we will,
however, assume there is an imaginary subsampling of cells by the subselection
of one out of a total of one cell per PSU. The procedures for selecting
housing units, households and individuals are exactly like the ones applied
elsewhere in the survey.
Stratification of PSUs
AJ is subdivided into 28 "statistical areas" having Arabs (nonIsraelis)
as the majority population. Israelis living within the PSUs are not considered
part of the survey population. The 28 areas constitute our PSUs. The areas
are those displayed in the Statistical Yearbook of Jerusalem 1990^{7}, with
a map dated 1983. Cell contours have, however, been transferred to updated
maps (1990) to make infield identification of the areas more easy. Cell
numbers refer to the numbers on the 1983 map (other statistical maps have
different numbers). The PSUs were grouped into 3 strata. The choice of location
(North, Middle, South) as the stratification variable is somewhat arbitrary,
and is not expected to yield reliability gains. However, it was considered
safe to make sure that all main districts of AJ were represented in the
sample. Table A.10 shows the stratification and the estimated population
1990 of each stratum (source: Statistical Yearbook of Jerusalem 1990).
Table A.10 Stratification of Arab Jerusalem PSUs
Stratum  Number of PSUs  PSUs (cell numbers)  Population 1990 
(s)  K(s)  (s,k)  N(s) 
North  7  711, 712, 713, 714, 715, 716, 717  39,100 
Middle  16  611, 621, 641, 642, 643, 751, 752, 753, 754, 761, 762, 763, 811, 812, 813, 814  82,900 
South  5  545, 821, 822, 823, 824  19,200 
First Stage Sample of PSUs
A sample of k(s) PSUs was selected within each stratum. The PSUs were selected
with probabilities proportionate to estimated population size:
where N(s,k) and N(s) have the same meaning as earlier, namely the population
totals (individuals) for PSU (s,k) and stratum s, respectively. The number
of PSUs to be selected from each stratum has been decided this way as a
"compromise" between theoretical, statistical considerations and
cost/implementation effectiveness. The household sample (total 500) was
proportionately allocated among strata. The 1st stage inclusion probabilities
imply the stratum sample of households to be equally divided among sample
PSUs to have an (approximate) epsem allocation. The sample PSUs are listed
in table A.11 along with the corresponding household sample size and the
1990 population estimates as compiled from Statistical Yearbook of Jerusalem
1990.
Table A.11 Arab Jerusalem sample of PSUs, and PSU sample size (households)
Stratum  Sample PSUs  Sample size (households)  Population 1990 (individuals) 
(s)  (s,k)  d(s,k)  N(s,k) 
North  713  70  8,100 
"  716  70  5,600 
Middle  611  50  4,600 
"  752  50  7,600 
"  753  50  4,900 
"  754  50  5,900 
"  813  50  9,100 
"  814  50  9,300 
South  821  30  4,500 
"  823  30  6,900 
Inclusion Probabilities
According to the details described above, the overall (household) inclusion
probability (household (s,k,c,h,d)  the d'th household of the h'th housing
unit (of imaginary cell c) within PSU (s,k)) is:
where H(s,k,c) is the total number of housing units of PSU (s,k), and D(s,k,c,h)
the total number of households within housing unit (s,k,c,h). The various
H(s,k,c)s have to be estimated from sample observations and population figures:
where the N(s,k)s are referred in table A.11 and the is an estimate for
the average number of individuals per PSU (s,k) housing unit:
In (4.4) N(s,k,c,h) is the number of individuals in sample household (s,k,c,h).
(Strictly, h is the housing unit label. For the sample, however, it also
works as a household label as long as only one household is selected from
each sample housing unit.)
The overall inclusion probabilities for the individual samples are calculated
by multiplying (4.2) with the individual probabilities of selection at the
"5th" stage:
where W(s,k,c,h,d) and M(s,k,c,h,d) are the numbers of females and males
of age 15 years or more of household (s,k,c,h,d), respectively. These statistics
are deducted from the sample.
