The functions of Sample Design Section consist of the following work related to development of efficient sample designs of sample surveys/censuses to be conducted by Pakistan Bureau of Statistics or other agencies: –

1. Development of optimum sample designs for various socio-economic, demographic and agricultural sample surveys, keeping in view the objectives of the survey, significance level of estimates & margin of error desired, consistent with the available resources. This includes determination of sample size on scientific lines, formulation of stratification plan, allocation of sample size to different strata/sub-strata and selection of sample as per sampling scheme finalized/approved for different strata of the universe and sub-universes or domains of study.
2. Maintenance and preparation of sample list of urban/rural blocks/ Mouzas/ Villages/Dehs selected for various sample surveys from the four provinces of Pakistan, Azad Jammu & Kashmir and Gilgit Baltistan.
3. Preparation of instructions for enumerators/supervisors for listing of households/ establishments in sample areas and selection of ultimate sampling units from primary sampling units constituted in sample surveys.
4. Monitoring the coverage and methodology of selecting the ultimate sampling units from sample areas.
5. Development of sampling weights based on the coverage information in respect of each sample area enumerated in sample surveys.
6. Development of estimation procedures to generate estimates of population parameters and their variances, sampling errors and design effects of important characteristics for which data are collected through sample surveys.
7. Evaluation of survey results to know the efficiency of the estimates of important characteristics pertaining to sample surveys using latest computer software.
8. Rendering technical assistance in terms of developing optimum sample design for sample surveys/studies as per request from national and international agencies/ departments.

Sample Design Section provides Sample Design to all PBS regular surveys; few are given below:-

1. Pakistan Standard & Living Measurement Survey (PSLM)
2. Household Integrated Economic Survey (HIES)
3. Labor Force Survey (LFS)
4. Pakistan Demographic Survey (PDS)
5. Surveys under Rebasing of National Accounts 2015-16 (Rent Survey, Construction Survey, Other Private Services Survey (OPSS), Small Households Manufacturing Survey (SHMI) )
6. Agricultural Census

PBS also provides Sample Designing of ad-hoc Surveys requested by Government Departments, National and International Organizations; few surveys are given below:

1. Pakistan Demographic & Health Survey (PDHS)
2. Pakistan Maternal Mortality Survey (PMMS)
3. Provincial Multiple Indicator Cluster Survey (MICS)
4. Provincial Child Labour Survey (CLS)
5. Comprehensive Food Security and Livelihood Assessment Survey (FSLA)
6. Annual Status of Education Report (ASER)
7. Global Adult Tobacco Survey (GATS)
8. Provincial Baseline Health Survey by National Health Support Program (NHSP)
9. National Survey on The extend, pattern and trends of Drug Use Survey
10. Monitoring of Tobacco Control Compliance Survey
11. Punjab Homebased and Domestic worker survey

There are also various other small surveys/studies in which PBS provides technical support for sample designing and selection of ultimate sampling units.

NUMBER OF DIVISION, DISTRICT, TEHSIL

Total number of blocks – 2023 Population & Housing Census

1. Name of Province
2. Name of Division
3. Name of District
4. Name of Tehsil
5. Name of Qanungo Halqa/ Charge No.
6. Name of Patwar Circle/ Circle No.
7. Number of Households
8. Name of Village/Mauza/Deh/ MC/TC
9. Rural/Urban
10. Enumeration Block Code (E.Bs)

Pakistan Bureau of Statistics (PBS) conducts routine and ad-hoc surveys spanning national, provincial and district domains. The Labor Force Survey (LFS) and Pakistan Social and Living Standards Measurement Survey (PSLM) are district specific, the household Integrated Economic Survey (HIES) focus on provincial representation, while Pakistan Demographic Surveys ensures national representation. It is worth mentioning here that, PDS and HIES utilizes provinces as strata where as PSLM and LFS districts are used for stratification.

A two stage stratified sample design is often used in PBS regular household based surveys where PSUs/EBs are selected at first stage and certain number of households as Secondary Sampling Units (SSUs) at the second stage.

Primary Sampling Unit (PSU):

Enumeration blocks are taken as Primary Sampling Units (PSUs). Sample PSUs from each ultimate stratum/sub-stratum are selected with probability proportional to size (PPS). The number of households in an enumeration block is considered as measure of size (MOS).

Secondary Sampling Unit (SSU):

The total number of listed households of sample PSUs are taken as Secondary Sampling Units (SSUs). A specified number of households from each PSU are selected with equal probability using systematic random sampling technique with a random start.

Sample Size Estimation

For estimation of sample size; the core survey variables correlated to the survey objective and scope considered. The following formula used to estimate the sample size under simple random sampling

$$ n = \left(\frac{{4r(1-r)}}{{(RME \times r)^2}}\right) $$

Where,

n =            the required sample size, expressed as number of households

4 =            a factor to achieve the 95 percent level of confidence

r =            the predicted or anticipated value of the indicator

RME =      the relative margin of error

Generally, for the complex sample design, sample size inflated by incorporating the Design effect (Deff) and Response rate

$$ n = \frac{{4r(1-r)D_{\text{eff}}}}{{(RME \times r)^2} \times RR} $$

RR =         the predicted response rate

deff =       the design effect for the indicator

Sample Allocation/ Allocation Plan

After estimation of sample size; the sample size is further distributed into various stratum as per survey objectives, i.e province, division, district, Rural/Urban. Different types of allocation used as shown below.

1. Proportional Allocation
2. Power Allocation
3. Equal Allocation

Weighting Scheme

As per sampling scheme, Survey weights are developed for each stratum because different sampling fractions used in each stratum. For this reason, sample weights calculated, which later used in the subsequent analysis of the survey data. Sampling weight is the reciprocal of the sampling probabilities employed in selecting the number of sample households in that particular sampling stratum (h) and PSU (i):

$$ W_{\text{hi}} = 1/f_{\text{hi}} $$

The term f_hi, the sampling fraction for the i^th sample PSU in the h^th stratum, and defined as the product of the probabilities of selection at every stage in each sampling stratum:

$$ f_{\text{hi}} = p_{\text{1hi}} X {\text{2hi}} $$
Where p_shi is the probability of selection of the sampling unit at stage s for the i^th sample PSU in the h^th sampling stratum. Based on the sample design, the two stage probabilities of selection calculated as follows:

$$ ( p_{1hi} = \frac{n_h \times M_{hi}}{M_h} )$$,

where,

n_h =     number of sample PSUs selected in h^th stratum

M_hi =   number of households in the frame for the i^th sample PSU in the h^th stratum

M_h =    total number of households in the frame for h^th stratum

$$ ( p_{2hi} = \frac{m_hi }{M_hi} )$$,

where,

m_hi= take of certain households from each PSU

M’_hi =  number of households listed in the i^th sample PSU in the h^th stratum

As we know automation has enhanced efficiency, accuracy, and productivity in the organizations and it has also reduced human error and labour costs. Sample Design Section uses Sample Design Software developed by Data Processing Centre team of Pakistan Bureau of Statistics for the Selection of PSUs from Population & Housing Census 2023.

Industry Surveys

A single stage sample design is often used in PBS Industry based surveys where sampling frame is provided by the Business Register Section. Based on some specific variables, stratification are made. After selection of PSUs, all establishments/ industries are covered.

Sample surveys are planned and designed based on the objectives and requirements of data users. The following information is pre-requisite to design sample surveys precisely.

• Characteristics on which data is to be collected (variables of interests).
• Definition of study population (target population).
• Previous information about the study population in terms of variation in respect of characteristics obtained from a retrospective survey/census
• Desired precision to be achieved in the estimates.
• Geographic level of estimates (District/Division/ Province by urban and rural).
• Timeliness and cost of the survey.