Appendix ASampling StrategySteinar Tamsfoss
1 Introduction
As a matter of course, sample designing to a large extent relies on what
kind of information about the survey population is actually available at
the time of planning. Existing information can be utilized both for improving
the sample design in terms of statistical reliability and for reducing field
work costs. Except for the Gaza Strip, the only relevant information available
was population numbers for subdistricts and localities. The corresponding
figures for Gaza proved to be too outdated and unreliable for our purposes,
implying a separate strategy had to be designed for Gaza. However, as preparations
proceeded we became aware of unpublished population data for Gaza Strip
localities, which was of great benefit in the final stages of the design.
Ideally, one might have designed separate sampling strategies for each of
the surveys. On practical grounds, not least the high costs that would be
involved, this was considered unrealistic. Moreover, the additional advantages
that could be expected were clearly marginal from the point of view of representativity.
A combined design for all three surveys was chosen, adopting the following
conceptual approach:
According to Benvenisti^{1}, the Arab population totals for individuals of all ages for the three areas are shown in table A.1. Table A.1 Estimates of the permanent population (nonJewish) in the Gaza Strip, West Bank and Arab Jerusalem
Although these figures are estimates for the 1987 populations, and not very reliable ones at that, they should be able to give an indication of the relative distribution of the "permanent" population (including residents abroad for less than a year). No census has been taken in the occupied territories since 1967, and all population statistics are estimates. According to Benvenisti, an Israeli Central Bureau of Statistics estimate of the West Bank population amounted to 858,000 as of December 31, 1987. The Interior Ministry figure for the West Bank as of November 1987 was 1,252,000. A critical discussion of the three sets of figures are found in the cited Benvenisti publication. When comparing with other Israeli official statistics, no equivalent estimates are found. However, for the adult population the estimates in table A.2 can be extracted from these.^{2} ^{3} Table A.2 Estimates of the adult nonJewish population in the Gaza Strip, West Bank and Jerusalem
Obviously, it is difficult to compare the absolute magnitude of the two sets of population figures as the latter one is logically as well as numerically a subset of the former. Assuming that the proportions of adults within each area are about the same in the three areas, it is seen that the relative proportions in the tables above are not very different. For the purpose of the present survey  aiming at providing relative distributions rather than absolute numbers  the accuracy of the Benvenisti proportions is assumed to be fairly satisfactory, taking into account that estimates of relative distributions are more robust against distortions of the population proportions than are estimates of absolute magnitudes. The particular issue of "illegal" immigration to Arab Jerusalem (Palestinians living without proper permits) may serve as an illustration of some of the problems involved in evaluating the reliability of the various population estimates. According to official figures compiled by the Israeli security services, illegal immigration amounts to 10,000^{4}. Another estimate (probably originating from the Interior Ministry) was conveyed by Jerusalem City Councilman Shmuel Meir in an interview^{5}: "Some 100,000 Arabs from Judea and Samaria have moved to East Jerusalem since 1967, many illegally". A third estimate, reported by the Jerusalem Post the same winter, stated that "nearly 2,000 illegally built homes were discovered in East Jerusalem in a recent Interior Ministry survey which also showed tens of thousands of Arabs from the territories were living illegally in the capital." The evaluation problem does not merely lie in the difficulties in assessing which estimate is the most accurate one, but also in the uncertainty with regard to whether the illegal residents are included in the estimates or not. However confusing this unclear state of statistics may be, it should be made clear that this survey comprises the present population in the three areas  illegal residents included. One of the inherent survey objectives has been to analyze data for the three regions separately. For such analyses to be reliable a certain minimum number of observations has to be collected in each of the regions. For surveys comprising a wide range of variables a proportionate regional sample allocation is normally recommended as a compromise yielding fairly reliable allover estimates. However, for Arab Jerusalem a proportionate allocation would imply a sample size of only 175 observations (approximately 90 females), which is too small to support the reliability standards required. These standards were set to the equivalence of 500 (female sample 250) as the minimum number of observations for one single area. This measure obviously implied that the regional sample allocation would have to be disproportionate, and that considerations of optimality would make little sense. The regional sample allocation finally arrived at is shown in table A.3. Table A.3 Regional sample allocation.
The sample designs for each of the regions are described in detail in the subsequent sections. A general, selfexplanatory overview of the various sampling stages and the corresponding sampling units involved at each stage, is shown in Figure A.1 Figure A.1 Overview of the Sampling Stages and the corresponding Sampling Units at each Stage
The question of inclusion probabilities also needs to be considered (inclusion probability is the probability of an arbitrary unit of the population being included in the sample). As will be seen, inclusion probabilities for the various sampling units involved differ for more reasons than the fact that the regional sample allocation would have to vary. One major implication of variations in inclusion probabilities is that proper weights must be assigned to each of the observations in order to achieve unbiased survey results. In most cases the inversed inclusion probabilities or variates derived from these are chosen as the individual weights. Estimators (computational methods) are discussed in a separate section.


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