Survey ID Number
PSE-PCBS-PECS-1997-V1.0
Title
Expenditure and Consumption Survey 1997
Sampling Procedure
The target population in this sample survey comprises all households living in the West Bank and Gaza Strip, excluding nomads and students.
The sample design is a stratified two-stage design for households selected to be interviewed. At the first stage a sample of cells (PSUs) was selected from the PCBS master sample frame. At the second stage, a sample of households was selected after a complete household listing of the sampled cells.
Sample Design
Stratification
Four levels of stratification have been made:
Stratification by District.
Stratification by place of residence which comprises:
(a) Municipalities (b) Villages (c) Refugee Camps
Stratification by locality size.
Stratification by cell identification in that order.
Sample Size
The sample size is about 3,591 households allowing for non-response and related losses .
Target cluster size
The next important issue in the sample design is the target cluster size or “sample-take” which is the average number of households to be selected per PSU. In this survey, the sample take is around 10 households.
Self-weighting design:
At the first stage, clusters or “cells” have been selected with PPS probability proportional to estimated measure of size (Mi) for unit (I):
Where the summation covers all clusters in the population; a-300 is the total number of selected clusters. It is highly desirable for the PECS to have a constant overall sampling rate (f), i.e. to have a self- weighting sample. This requires the second stage probability for the selection of households and persons within any sample cluster i to be as follows:
Where b is a constant (independent of i) to be determined to obtain the required sample size, n =3,591 households. Since the measure of size are likely to differ from the actual number of households listed in any cluster i, the actual number of households selected with the above shall vary from one cluster to another and are presented as:
Adding all clusters in the sample results in the required constant b, to achieve the target sample size n as:
Hence to control the overall sample size, b is determined after completing the listing in all sample areas.
The above procedure allows for variation in sample sizes bi at the level of individual clusters, in order to provide a self-weighting sample. Households within each sample cluster shall be selected systematically from the lists prepared for that purpose, using the sampling interval,
Where:
a Number of cells in the sample (equals 360)
Number of housing units in cell I
Number of listed of households in cell I
n Proposed sample size (n= 3,591 HHs)
b Average sample take
Sample take in cell I
f Sample rate
First-stage sampling rate
Second-stage sampling rate
Which is fixed for each cluster but varies between clusters depending on the measure of size () with which the area was selected at the first stage.
The sample-take must be allowed to vary depending on the actual number of households found after listing. However, provision must be made to avoid extreme variation in cluster sample size. This could be done by using the above procedure to compute the ratio for each cluster in the sample. If this ratio lies outside the range say 0.5 - 4.0, adjust , i.e. the interval to be applied for the selection of households in the cluster, so as to keep the ratio within the above range.
Sample Rotation
The total number of (480) cells have been divided into (24) groups (subsided sample), each one constituted of (20) cells. A sub-sample of (360) cells is used year round by a monthly sample constituted of two minor samples (30 cells). The survey includes independent cells and not cross section ones, each of these is formed from (300) households for each month (round).
(Replication)
L K J I H G F E D C B A Month
× 1
× 2
× 3
× 4
× 5
× 6
× 7
× 8
× 9
× 10
× 11
× 12
Estimations Procedure
The sample is self-weighting by design. To estimate a given total Y for a given sub-population A, we introduce the following formula:
But since W is constant for all j within i, then: the estimating formula becomes:
Where,
U
YA = Estimated total for variable Y in sub-population A
h = The sub-stratum within the estimation domain
i = The sample PSU (cell)
j = The unit of analysis or element
A = Subset of elements possessing a given attribute, that is, belonging to a given sub- population A
= Observed value of variable “y” for j-the element of i-the sample PSU in stratum h
= Final (adjusted) sampling weight for the element
is the unweighted PSU total within h for sub-population A
The estimator for a given ratio for sub-population A is the following:
(2)
Where:
U
RA =Estimate for the ratio of two variables, Y/X, in sub-population A
U
XA = Estimated total for variable X in sub-population A, given by formula (1)B
U
YA = Estimated total for variable Y in sub-population A, also given by formula (1)B
Means and proportions are special types of ratios. In the case of the mean, the variable X, in the denominator of the ratio, is defined to equal 1 for each element, so that denominator is the sum of weights in the sub-population.
In the case of the proportion, the variable X in the denominator is also defined to equal 1 for all elements. In addition, the variable Y in the numerator is binomial and is defined to equal either 0 or 1, depending on the absence or presence of a specified attribute in the element observed.
Calculation of Variance
It is very important to calculate standard errors for the main survey estimates so that the user can have an idea of their reliability or precision.
The variance calculation will use the method of ultimate clusters. Within any domain of estimation, for a sub-population A, and for a characteristic Y, the formulas are:
(a) The variance of an estimator of a total is estimated by:
(3)
Where:
(4)
and:
(5)
The expression in (3) is an unbiased estimator of the variance.
(b) The variance of an estimator of a ratio is estimated by:
(6)
Where:
U U
V (YA) and V(XA) are calculated according to formula (3);
U
XA is calculated according to formula (1); and
U
RA according to formula (2).