Developing a Master Sample Design for Household Surveys in Developing Countries: A Case Study in Bangladesh

Dalisay S. Maligalig, Asian Development Bank Institute
Arturo Martinez Jr., University of Queensland

12.07.2013
How to cite this article:

Maligalig, D. S., & Martinez, A. Jr (2013). Developing a Master Sample Design for Households Surveys in Developing Countries: A Case Study In Bangladesh. Survey Methods: Insights from the Field. Retrieved from http://surveyinsights.org/?p=2151

Copyright:

© the authors 2013. This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0) Creative Commons License


Abstract

For evidence-based policy making, socio-economic planners need reliable data to evaluate existing economic policies. While household surveys can serve as a rich source of socio-economic data, conducting them often entails a great deal of administrative, technical and financial resources. With limited resources for data collection, this often puts pressure on national statistical systems to meet the continuously growing data demand of its stakeholders, especially in developing countries. Using a master sample design that can be used to select samples for multiple household surveys provides an opportunity to minimize the resources needed to collect household survey data regularly. In particular, using the same sampling design and frame to select samples either for multiple surveys of different content or for different rounds of the same survey could induce significant cost-savings instead of developing an independent design each time a household survey is to be carried out. This paper provides a step-by-step guide for developing a master sample design for household surveys in developing countries. Using Bangladesh as a case study, issues like effective sample allocation to ensure the reliability of domain estimates, stratification measures to reduce design effects and introducing household sample size adjustment when to maintain uniform selection probability within domain are discussed.

Keywords

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Acknowledgement

This study was funded by Asian Development Bank’s Regional Technical Assistance (RETA) 6430: Measuring the Informal Sector. In general, ADB RETAs aim to build, strengthen and improve statistical systems and services of the Bank’s developing member countries. The study also acknowledges the valuable inputs and coordination efforts of the management and staff of Bangladesh Bureau of Statistics particularly Ms. Mir Suraiya Arzoo, Mr. Nowsher Ahmed Chowdry, Mr. Ghose Subobrata, Mr. Mohammad Abdul Kadir Miah, Mr. Md. Rafique Islam, Mr. Kabir Uddin Ahmen and Ms. Sabila Kahtun.


Copyright

© the authors 2013. This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0) Creative Commons License

Copyright

© the authors 2013. This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0) Creative Commons License


1. Background

Household surveys have been important source of various socio-economic information that are indispensable in development planning and policy analysis. In some countries, especially developing ones, household surveys have become more dominant form of data collection than other administrative data collection programs such as civil registration systems (UNSD 2005). Thus, there is a need to ensure that household surveys follow scientifically-sound design to assure the quality of information that can be derived from it. While many countries have put in place national statistical systems for collecting household surveys, they have varying levels of experience and infrastructure in data collection. Many developing countries usually confront budgetary constraints and thus, heavily rely on technical assistance from international development agencies. To promote sustainability of statistical data collection activities, different strategies have been proposed to economize the technical and financial resources needed for collecting household surveys. One of these strategies is the development of a master sample design. For multi-stage household surveys, a master sample design allows one or more stages to be combined or shared among different household surveys. In turn, a master sample refers to the sample resulting from the shared stages (UNSD 2005). The UNSD (2005) identified several advantages of adopting a master sample design. First, it reduces costs of developing and maintaining sampling frames as more household surveys share the same master sample design. It also simplifies the technical process of drawing individual samples by facilitating operational linkages between different surveys. In this study, we document our experiences in helping Bangladesh develop a master sample design for collecting household surveys.

The Bangladesh Bureau of Statistics (BBS) is the government agency mandated to undertake data collection for the compilation of official statistics for Bangladesh. Household surveys of national coverage are the primary data collection tool of BBS. Prior to the 2009-2010 Labour Force Survey, the 2005 LFS and 2005 Household Income and Expenditure Survey (HIES) were the last household surveys conducted by BBS, both of which employed the Integrated Multi-Purpose Sampling Design (IMPS). However, previous studies such as that of Maligalig and Barcenas (2008) identified technical deficiencies in IMPS. In particular, large design effects were derived for important characteristics of interest such as unemployment rate in the statistical metropolitan areas (SMA) and for large divisions such as Dhaka, Chittagong and Rajshahi because of ineffective stratification measures. In addition, the survey weights used in IMPS did not reflect the selection probabilities that were applied at the time when the sampled households were drawn. Moreover, Maligalig and Barcenas (2008) also noted that the number of households sampled per primary sampling unit (PSU) can still be reduced and the number of PSUs increased to mitigate the very large design effects. Due to these issues, BBS requested technical assistance from Asian Development Bank in 2008 to develop a new sampling design and sampling frame that could be used for the then forthcoming 2009-2010 Labour Force Survey. Moreover, the main objective of the activity is to re-implement the proposed sampling design once the data from the 2011 Census of Population becomes available. In turn, the updated version will serve as master sample design for the succeeding household surveys that BBS will conduct. This paper documents the processes that were undertaken to develop the sample design for 2009-2010 LFS which will also be the basis for a new master sample design. The study aims to provide survey statisticians from developing countries with empirical guidelines in developing a master survey design for multiple household surveys.

After this introduction, the succeeding discussions are outlined as follows. Section 2 provides a guide for constructing primary sampling units for household surveys. Section 3 identifies the statistical and practical issues that must be considered in designating the survey domain. Section 4 discusses survey stratification as a tool for improving precision of survey estimators. Section 5 discusses sample selection schemes that control for design effects of complex surveys. The last section provides a brief summary of the discussions.

2. Sampling Frame of the Primary Sampling Units

Multi-stage sampling is usually the most appropriate, cost effective and commonly used design for household surveys of national coverage in developing countries. Households (or housing dwellings) are the ultimate sampling units while the primary sampling units (PSUs) are usually clusters of contiguous households. Although stratified simple random sampling is perhaps the most efficient among the conventional sampling designs, it is not practical and workable for most household surveys in developing countries because an updated list of all households in a country is not commonly available. In general, a good sampling frame is needed to ensure that each ultimate sampling unit has a chance of being selected and hence, conclusions on the target population can be drawn from the sample.

Constructing a frame of the primary sampling units is the first step in developing a multi-stage sampling design. At this point, it is important to decide carefully on what should be designated as the PSU. There are several considerations. Ideally, all units in the target population should belong to one and only one of the PSUs. To this end, PSUs must  have clear boundaries which can be easily located in the field. In addition, auxiliary information about the “size” of the PSU to be used for selecting which unit will be in the sample should be available. If the total number of households is used as measure of PSU’s size, a PSU has to be as manageably small as possible but large enough to have adequate number of ultimate sampling units. This would permit sampling rotations for different surveys which will be implementing the master sample design. Moreover, availability of information to be used for stratification and sample allocation should also be among the practical considerations in constructing the PSUs.

In Bangladesh, unions, mauza, villages and enumeration areas as defined in the 2001 Census of Population are possible candidates for designating PSU. However, preliminary analysis shows that unions vary widely in size and in general, they are too large to permit manageable field operations. Villages, on the other hand, are almost the same as enumeration areas for rural areas and their boundaries are not clear in the case of urban areas. Given this information, only mauza and enumeration areas were considered for PSUs in the succeeding discussions. Using data from the 2001 Census of Population, Tables 1 and 2 summarize the distribution of the number of households by mauza, and by enumeration area, respectively. Noticeably, the total number of households vary widely at the mauza level, from 1 to 22,366 (Other Urban Areas, Dhaka). If mauza is designated as the PSU, then some mauzas will still have to be divided further to ensure that each PSU will not be selected more than once. At the same time, some mauzas may need to be combined to ensure that there is sufficient number of households that can be drawn from each PSU. In contrast, although there are still many enumeration areas that need to be combined if they are designated as PSUs, enumeration areas need not be broken down further since the maximum total number of households per enumeration areas is 497 (Table 2). Thus, forming PSUs using the enumeration areas presents a better option than designating mauzas as PSUs.

Table 1. Summary statistics of total household of Bangladesh by Mauza

Division No. of Mauzas Urban block No. of Mauzas by block Distribution of the Number of Households by Mauza
Total Min Median Mean Max Std dev
Barisal 3414 Rural                          2,896 1,411,766 1 321 487.49 5,126 481.19
Urban block                             419 144,911 11 249 345.85 3,196 333.86
SMA                              99 91,408 26 718 923.31 4,342 794.92
Other urban areas
Chittagong 8879 Rural                          7,367 3,317,141 1 258 450.27 11,943 600.50
Urban block                          1,175 743,076 1 284 632.41 9,831 1,130.94
SMA                             207 257,432 9 794 1,243.63 8,045 1,398.13
Other urban areas                             130 154,899 10 823 1,191.53 5,328 1,208.63
Dhaka 18295 Rural                        14,660 5,399,312 1 219 368.30 8,820 473.40
Urban block                          2,616 1,824,745 1 303 697.53 9,218 1,175.43
SMA 289 254,248 1 576 879.75 5,325 952.55
Other urban areas 730 758,382 1 316 1,038.88 22,366 2,283.58
Khulna 7483 Rural 6,300 2,472,098 1 264 392.04 5,119 422.51
Urban block 913 433,156 1 307 474.43 5,823 544.95
SMA 166 131,468 51 583 791.98 4,101 705.05
Other urban areas 105 82,880 1 408 789.33 4,938 1,015.84
Rajshahi 18887 Rural 16,423 5,643,537 1 221 343.64 5,758 382.17
Urban block 1,951 645,620 1 232 330.92 2,597 304.51
SMA 340 280,392 5 588 824.68 4,042 703.76
Other urban areas 173 58,248 1 278 336.69 2,026 301.33
Sylhet 5708 Rural 4,989 1,213,085 1 167 243.15 3,052 256.24
Urban block 608 110,982 1 136 182.54 1,328 166.86
SMA 111 64,155 20 427 577.97 2,865 559.31
Other urban areas

Source: Authors’ computations using data from 2001 Census of Population conducted by BBS

Table 2. Summary statistics of total household of Bangladesh by Mauza

Division Urban block No. of enumeration areas Households
Total Min Median Mean Max Std dev
Barisal Rural 14,473 1,411,766 1 96 97.54 354 25.58
Urban block 1,573 144,911 1 88 92.12 233 29.94
SMA 898 91,408 2 98 101.79 267 28.13
Other urban areas
Chittagong Rural 36,172 3,317,141 1 94 91.70 321 34.25
Urban block 7,943 743,076 1 92 93.55 339 31.73
SMA 2,997 257,432 1 87 85.90 237 39.46
Other urban areas 1,428 154,899 2 107 108.47 310 35.52
Dhaka Rural 54,822 5,399,312 1 99 98.49 483 31.38
Urban block 18,819 1,824,745 1 93 96.96 471 37.97
SMA 2,418 254,248 1 102 105.15 404 36.49
Other urban areas 7,030 758,382 1 100 107.88 478 43.49
Khulna Rural 23,530 2,472,098 1 104 105.06 320 30.28
Urban block 3,998 433,156 1 103 108.34 344 35.53
SMA 1,187 131,468 8 108 110.76 239 31.07
Other urban areas 744 82,880 1 106 111.40 305 34.66
Rajshahi Rural 55,004 5,643,537 1 101 102.60 463 29.94
Urban block 6,707 645,620 1 93 96.26 497 35.07
SMA 2,639 280,392 1 103 106.25 286 33.12
Other urban areas 546 58,248 1 104 106.68 295 34.59
Sylhet Rural 14,875 1,213,085 1 84 81.55 258 36.29
Urban block 1,302 110,982 1 84.5 85.24 276 39.11
SMA 723 64,155 1 90 88.73 258 37.99
Other urban areas

As mentioned earlier, it is ideal for every PSU to be large enough to have adequate number of ultimate sampling units to ensure the feasibility of adopting a rotating sample design for different surveys which will be implementing the master sample. In the case of Bangladesh, we set the threshold to be 40 households per PSU. Out of the 259,828 EAs, 12,273 EAs have less than 40 households. These small EAs should be considered as candidates for merging. When combining small EAs to form PSUs, the main consideration is that the enumeration areas to be combined are contiguous. However, due to the lack of reliable (geographic) maps for these EAs, we decided to combine the small enumeration areas based on the criteria provided below. In addition, due to the conceptual and logistical problems in the classification of statistical metropolitan areas (SMA) and other urban areas, it was decided that these two areas will be classified under urban area instead.

Criteria for combining enumeration areas to form a primary sampling unit

  1. An EA with more than 40 households is directly considered as a PSU.
  2. A small EA is attached to an adjacent EA that belongs to the same urban/rural classification and mauza.
  3. A small single EA in a mauza can be combined with an EA of another mauza provided that both mauzas belong to the same union and the EAs to be combined belong to the same urban/rural category.

Following this criteria, a total of 248,904 PSUs were constructed out of the 259,828 original EAs. Table 3 provides the distribution of the number of households by PSU. As shown in this table, there are still PSUs that have less than 40 households. These correspond to cases where the unions were very small in terms of number of households. Since these very small units constitute only of 11 PSUs, we decided to exclude them from the sampling frame.

Table 3. Summary statistics of total household of Bangladesh by PSU

Division Urban block No. of PSUs Households
Total Min Median Mean Max Std dev
Barisal Rural 14,280 1,411,766 41 97 98.86 354 24.30
Barisal Urban 2,414 236,319 42 94 97.90 267 27.36
Chittagong Rural 33,721 3,317,141 41 97 98.37 321 28.17
Chittagong* Urban 11,810 1,155,407 23 95 97.84 339 30.98
Dhaka Rural 52,667 5,399,312 19 100 102.52 483 27.88
Dhaka* Urban 27,317 2,837,375 21 98 103.88 478 36.93
Khulna Rural 22,886 2,472,098 31 105 108.02 320 27.01
Khulna Urban 5,823 647,504 41 105 111.20 344 32.69
Rajshahi Rural 53,554 5,643,537 41 102 105.38 463 27.28
Rajshahi Urban 9,614 984,260 13 98 102.38 497 32.20
Sylhet Rural 12,992 1,213,085 41 92 93.37 266 29.79
Sylhet Urban 1,826 175,137 21 93 95.91 296 33.27

Source: Authors’ computations using data from 2001 Census of Population conducted by BBS.

Notes: * – There are 3 PSUs that have very few number of identified households on the basis of the latest census data. In particular there are one PSU from Chittagong (urban) and two from Dhaka (urban) that have less than 10 households. These were not included in the computation of summary statistics provided above.

3. Survey Strata, Determination of Sample size and Sample Allocation

Design domains or explicit strata are subpopulations for which separate samples are planned, designed and selected (Kish, 1987). The choice of explicit strata depends on several factors such as reporting requirements, sampling design and more importantly, available budget and workload that will be used (Kish, 1965;1987). Both statistical and practical issues must be considered in designating the strata. In general, there is now greater demand for statistics at finer levels of disaggregation (Elbers, Lanjouw and Lanjouw 2003). In turn, this would require increasing the number of strata. Since the total sample size is usually determined at the stratum level, increasing the number of strata would necessarily entail increasing the total sample size. Because the workable sampling designs would all involve cluster sampling, the expected design effects should also be considered and used to determine the final sample size. Average design effects for cluster samples is expected to be three or more and hence, the final sample size would have to be increased by this value. However, these things should be contextualized within the available budget allocated for survey data collection.

Once the strata have been clearly specified, the sample size for each stratum is then determined so that reliable estimates at the stratum level can be derived. Information on the variability of the sampling units within each stratum, the acceptable error level, and the associated costs are the factors needed to determine the sample size. For example, suppose the primary characteristic of interest to be measured can be expressed as a proportion. Under simple random sampling (SRS), the tentative sample size for a particular stratum is computed such that

(1)   \begin{equation*} n{_{srs}}=\frac{\frac{t_{(\alpha, N-1)}^{2}P(1-P)}{d^{2}}}{1+\frac{1}{N}(\frac{t_{(\alpha, N-1)}^{2}P(1-P)}{d^{2}}-1)}, \end{equation*}

where t_{(\alpha, N-1)} is the abscissa of the t-distribution given risk \alpha, and the population size N; P is the true proportion of the characteristic of interest and error level d (Cochran, 1977). Since P is unknown, we can either set P = 0.5 or used any prior information about the value of P from previous studies. Note that setting P = 0.5 would produce the most conservative or largest sample size. The resulting sample sizes on the application of (1) are then inflated by the corresponding design effects (Deff), assuming that prior information about the magnitude of the design effect is available.

(2)   \begin{equation*} n_{complex} = \text{Deff}*n_{SRS}. \end{equation*}

In the case of Bangladesh, the geographic divisions were designated as the design domains or explicit strata. If the 64 zilas (provinces) were specified as the strata, the sample size required will be inflated by approximately ten times and that would be beyond the budget of BBS. Moreover, we used the estimated unemployment rate using the 2005 LFS to provide a value for P. Table 4 shows the tentative sample sizes that were computed at risk \alpha = 0.05 and varying error level d. The corresponding design effects of unemployment rates from the 2005 LFS are also shown in Table 4. Note that at d=0.01, the total sample size is 115,277. This sample size is 100,000 more households than what the budget of BBS has allocated for the 2009-2010 LFS can afford. At d=0.03, which may not be very appropriate considering that unemployment rates are quite small, the total sample size is about 12,814 households or within budget. The total sample size became very large because of large design effects especially for Dhaka and Khulna. The perceived large variability among these divisions may not really reflect the large variation across households in these divisions but the wide variation in the artificial weights that were attributed to the households. Given this backdrop, the sample sizes that were computed in Table 4 were used only as guides for determining the final total sample size. In particular, we proposed to sample 10 households per PSU following the recommendation of Maligalig and Barcenas (2008) instead of the 40 households per PSU followed in IMPS. This allows us to increase the number of sampled PSU from 1000 in IMPS to 1500 in the new sample design. Considering that there is positive intra-correlation among households in the same PSU, then increasing the number of sampled PSU while reducing the number of sampled household per PSU is deemed reasonable.

If the survey weights used to compute the sample size in Table 4 were correct, the estimates at the division level will have margin of error of about .03. This is not acceptable since this error level is quite large considering that division level unemployment rates only varies from .01 (Sylhet) to .06 (Barisal). On the other hand, since the survey weights in the 2005 LFS have technical flaws and stratification measures used were not effective in controlling the design effects, the resulting estimates from the 2009-2010 LFS using the proposed master sample design can still render acceptable design effects even with only 15,000 households total sample size. This favorable outcome depends on the quality of implementation of a better design for the master sample, specification of the correct survey weights and better stratification.

Table 4. Tentative Sample Sizes

Division Unemployment Rate # of households DEFF SRS sample size Sample size: Complex survey
d=0.05 d=0.03 d=0.01 d=0.05 d=0.03 d=0.01
Barisal 0.0622 1,648,085 5.12 89.57 248.77 2236.24 460.31 1278.51 11492.75
Chittagong 0.0461 4,472,548 8.38 67.51 187.53 1687.17 567.31 1575.81 14177.52
Dhaka 0.0474 8,236,687 27.00 69.37 192.70 1733.99 1878.49 5217.95 46952.74
Khuha 0.0545 3,119,602 18.58 79.18 219.92 1978.19 1475.64 4098.83 36868.64
Rajshahi 0.0311 6,627,797 3.41 46.26 128.51 1156.41 158.07 439.08 3951.07
Sylhet 0.0182 1,388,222 2.66 27.53 76.47 687.90 73.40 203.88 1834.07
Total 4613.22 12814.05 115276.79

Source: Authors’ computations using data from 2005 LFS conducted by BBS.

Several allocation strategies were examined to allocate the 15,000 sample households across domains: equal allocation, proportional allocation, square root allocation and Kish allocation.

Equal Allocation:

    \begin{equation*} n_{d} = \frac{n}{D} =\frac{n}{6} \end{equation*}

Proportional Allocation:

    \begin{equation*} n_{d} = n\frac{N_d}{N} =nW_{d} \end{equation*}

Square Root Allocation:

    \begin{equation*} n_{d} = n\frac{\sqrt{N_d}}{\sum_{m}\sqrt{N_m}} \end{equation*}

Kish Allocation:

    \begin{equation*} n_{d} = n\frac{\sqrt{D^{-2}+IW_{d}^{2}}}{\sum_{m}{\sqrt{D^{-2}+IW_{m}^{2}}}} = n\frac{\sqrt{\frac{1}{36}+IW_{d}^{2}}}{\sum_{m}\sqrt{\frac{1}{36}+IW_{m}^{2}}} \end{equation*}

where n_d is the sample size in the domain, n is the sample size, D is the number of domains, N_d is the total number of households in domain d, N is the total number of households in Bangladesh, per the 2001 Census of Population, W_d is the proportion of households in domain d, and I is the Kish allocation index denoting the relative importance assigned to estimates at the national or subgroups that cut across domains (type (i)) as compared to those estimates at the domain levels (type (ii)). To illustrate, we can relate (i) to characteristics of interest such as numbers of crop farmers and female unpaid workers, proportions of persons in poverty in Bangladesh, number of persons in the labor force who are unemployed, proportion of households with electricity, and estimates of the differences between subgroups. When computed at the domain level, these become type (ii) parameters. If the primary interest is to derive estimates for characteristics of interest of type (ii), one of the best approaches in allocating the total sample size is to allocate it proportionally with respect to the population size of each domain. However, the ideal approach for type (ii) is to divide the total sample size equally among the domains (Kish, 1987). Moreover, it should be emphasized that these two approaches may yield very different sample allocations particularly when the domains differ in measure of size. Further, it is possible that a particular approach may perform satisfactorily when estimating a certain type of characteristic of interest but not necessarily for the other types. A possible way around this problem is to use Kish allocation which is basically a compromise between equal and proportional allocation. With I = 0, it reduces to the equal allocation while it tends to proportional allocation approach with I \rightarrow \infty. Table 5 provides estimates of sample size per domain using different allocation procedures. Kish allocation at I = 1 was chosen to ensure that precision of both type (i) and type (ii) characteristics of interest will be approximately the same.

Table 5. Sample Allocation of Number of Sample Households per Domain

Division

(d)

Total
Households

N_d

W_d

Equal
Allocation

\frac{n}{6}

Proportional
Allocation

nW_d

Square root
Allocation

n\frac{\sqrt{N_d}}{\sum_{m}\sqrt{N_m}}

Kish
Allocation
(I=1)

n\frac{\sqrt{\frac{1}{36}+W_d^2}}{\sum_{m}\sqrt{\frac{1}{36}+W_m^2}}

Barisal

1,648,085

                     0.064649

                                2,500

                               969.73

                             1,633.65

1,817.68

Chittagong

4,472,548

                     0.175443

                                2,500

                            2,631.64

                             2,691.21

2,460.51

Dhaka

8,236,687

                     0.323097

                                2,500

                            4,846.45

                             3,652.13

3,696.56

Khulna

                                3,119,602

                     0.122371

                                2,500

                            1,835.57

                             2,247.60

2,102.39

Rajshahi

6,627,797

                     0.259986

                                2,500

                            3,899.78

                             3,276.08

3,140.06

Sylhet

1,388,222

                     0.054455

                                2,500

                               816.83

                             1,499.34

1,782.81

Bangladesh

25,492,941

                     1.000000

                              15,000

                          15,000.00

                           15,000.00

15,000.00

Source: Authors’ computations using different sample allocation procedure.

4. Implicit stratification of Primary Sampling Units

(Implicit) Stratification of PSUs is critical to ensuring that the (limited) sample size afforded by BBS will still render reliable estimates at the domain level and those that cut across domains. Ideally, a implicit stratification measure should be available and measured consistently for all PSUs in the domain. Examples of such stratification measures are geographical information such as zila (provinces) and urban/rural areas since each PSU carry the provincial code as well as the urban/area classification. Further stratification may be applied to ensure that the final groups of PSUs are more homogeneous. The candidates for stratification measures that are available for all PSUs are those variables that are in the 2001 Census of Population. In addition, an effective stratification measure is one that is highly correlated with major characteristics of interest in the survey. Those perceived to be correlated to income and employment which are the major characteristics of interests in LFS includes the proportion of households with strong housing materials (PStrong), proportion of households with agriculture as major source of income (PAgri); and proportion of households that own agricultural land (POal). Table 6 present the summary statistics for these three variables by division and rural/urban classification.

Table 6. Summary Statistics of Stratification Measures by Division and Urban/Rural

Division Stratification
Measures
Urban/Rural Minimum Median Mean Max Standard
Deviation
Barisal PStrong Rural 0 0.99 2.93 100 7.11
Urban 0 14.93 25.37 100 26.45
PAgri Rural 0 61.68 59.75 100 23.59
Urban 0 7.75 20.33 100 24.91
POal Rural 0 69.46 66.26 100 22.92
Urban 0 50.57 50.46 100 23.62
Chittagong PStrong Rural 0 4.05 7.46 100 10.70
Urban 0 30.48 38.11 100 31.68
PAgri Rural 0 46.94 48.99 100 25.85
Urban 0 4.55 15.21 100 22.29
POal Rural 0 58.33 57.26 100 22.87
Urban 0 38.63 40.41 100 25.21
Dhaka PStrong Rural 0 1.85 5.37 100 9.49
Urban 0 57.56 53.90 100 35.59
PAgri Rural 0 67.42 62.93 100 24.50
Urban 0 1.25 10.24 100 19.36
POal Rural 0 61.54 61.37 100 20.77
Urban 0 48.54 48.32 100 26.22
Khulna PStrong Rural 0 15.27 17.87 100 14.37
Urban 0 44.17 46.28 100 27.19
PAgri Rural 0 71.07 65.90 100 22.95
Urban 0 6.49 19.61 100 25.59
POal Rural 0 61.17 60.87 100 20.36
Urban 0 43.33 44.54 100 22.60
Rajshahi PStrong Rural 0 3.80 7.68 100 11.05
Urban 0 33.33 39.39 100 30.84
PAgri Rural 0 76.09 70.46 100 22.39
Urban 0 12.00 24.86 100 27.29
POal Rural 0 57.03 57.14 100 19.51
Urban 0 39.39 40.72 100 20.87
Sylhet PStrong Rural 0 11.83 17.92 100 18.68
Urban 0 49.07 47.42 100 29.50
PAgri Rural 0 58.76 56.09 100 28.57
Urban 0 7.25 18.55 100 23.43
POal Rural 0 49.38 49.36 100 22.63
Urban 0 38.65 40.68 100 22.71
Bangladesh PStrong All 0 6.06 17.47 100 25.36
PAgri All 0 56.82 51.12 100 31.86
POal All 0 56.43 55.64 100 23.06

Source: Authors’ computations using data from 2001 Census of Population conducted by BBS.

There are several findings that may be indicative that the urban/rural classification should be reviewed carefully. In particular, there are PSUs for urban areas in which all households have agriculture as main source of income while there are PSUs in rural areas with not even one household that has agriculture as main source of income. Table 6 also shows that ownership of agricultural land is not a very good distinguishing factor for urban/rural areas. This probably shows that there are many owners in urban areas who rent or lease their agricultural land and hence, decreasing the value of POal as a stratification measure.

As indicated by the standard deviation, minimum, median and maximum values, PStrong does not vary widely in rural areas. On the average, there is considerably much lower proportion of households that have strong housing materials in the rural areas. On the other hand, although the variation of PAgri is about the same for urban and rural areas in some divisions, the number of households with agriculture as main source of income is significantly much lower in the urban areas, on the average. These results prompted us to stratify urban areas using PStrong and rural areas using PAgri. In particular, since the numbers of households and PSUs in rural areas are more than twice those of the urban areas, four and two strata were planned for rural and urban areas, respectively. Strata boundaries were first set as the quartiles of PAgri for rural areas and the median of PStrong for urban areas. However, small strata or those that have total households that is less than the division’s sampling interval are combined with the adjacent strata. The number of PSUs for each of the 336 strata that were formed are summarized in Appendix 3.

In general, the key advantage of the (implicit) stratification procedure adopted here is that it is straightforward to implement and provide satisfactory results. Nevertheless, future studies may consider implementing more optimal stratification procedures such as those proposed by Sethi (1963) and Kozak (2004).

 

5. Sample Selection

Another measure for controlling design effect is to ensure that the survey weights within the domains do not vary widely. A wide variation of weights within a domain will unnecessarily contribute to the increase of variances of estimates. Hence, survey statisticians usually opt to maintain almost similar base weights within a domain. Since base weight is the inverse of the selection probability of an ultimate sampling unit, then maintaining similar or almost uniform base weights is tantamount to maintaining the same or almost the same selection probabilities within a domain. This section discusses the procedures on how this can be achieved. Here, we propose a simple two-stage sampling design such that in a domain d: (i) PSU \alpha will be selected with probability proportional to size and (ii) household \beta from PSU \alpha will be selected by simple random or systematic sampling, in a domain d in which all PSUs are also grouped into implicit strata. Thus, in domain d and (implicit) stratum h, the uniform selection probability f_d that a household is selected from PSU \alpha will be:

(3)   \begin{equation*} f_{d} = \frac{n_{d}^{'}}{M_{d}}, \end{equation*}

,

where n^{\prime}_d is the total sample size for domain d as defined in the last column of Table 5 (Kish Allocation, Index=1), M_d is the measure of size for domain d (i.e., total number of households per division based on the 2001 Census of Population data) and M_{h\alpha} is the measure of size for PSU \alpha at stratum h (i.e., total number of households for PSU \alpha from stratum h),

(4)   \begin{equation*} M_{d} = \sum_{h} \sum_{\alpha}{M_{h\alpha}}. \end{equation*}

In a two-stage cluster sampling design,

(5)   \begin{equation*} f_{d} = P( \alpha\beta|h) = P(\alpha|h)P(\beta|h\alpha), \end{equation*}

where P(\alpha|\h) is the selection probability of PSU \alpha and P(\beta|h\alpha) is the probability of selecting household \beta given PSU \alpha in stratum h is selected. Hence,

(6)   \begin{equation*} f_{d} = \frac{a_{h}M_{h\alpha}}{\sum M_{h\alpha}}\frac{b_{h}}{M_{h\alpha}} = \frac{a_{h}b_{h}}{\sum M_{h\alpha }}, \end{equation*}

where a_h is the number of PSUs to be sampled from stratum h, and b_h is the number of households to be selected from stratum h.

The term P(h\beta|\alpha)=\frac{b_{h}}{M_{h\alpha}} represents the sampling fraction to be used in the systematic sampling of households at the final sampling stage. Its inverse is the sampling interval to be applied in the selection of households from the sampled PSUs.

Considering (6), f_{d} will be uniform in a domain when \frac{a_{h}}{\sum M_{h\alpha}} and b_h do not depend on stratum h and hence, are both constant across all strata in domain d. Since the recommendation that b_h=10 for all sampled PSUs will be implemented, and if \frac{a_{h}}{\sum M_{h\alpha}} can be maintained to remain constant, f_{d} will be uniform in domain d. To do latter, the number of PSUs to be selected for stratum h, a_h must be proportional to the stratum h measure of size \sum M_{h\alpha}, which is actually the 2001 Census of Population total number of households for stratum h. However, since a_h must be a whole number and the strata measure of sizes also vary, the resulting selection probabilities across strata in domain d will not be totally the same but will not vary widely.

To maintain a uniform f_{d} in the whole domain, the same sampling interval can be applied on the list of all PSUs that are already sorted by strata. This implies that the selection of PSUs will not be done separately for each stratum in a domain but rather, will be performed collectively for all of the strata. The step-by-step procedure for maintaining a uniform selection probability within the domain is outlined below. Table 7 below shows the resulting uniform selection probabilities for each domain.

Sample Selection of Primary Sampling Units

(1) For a domain d, determine the number of PSUs to be sampled a_{d}^{'}, such that a_{d}^{'}=\frac{n_{d}^{'}}{b}, where b is the recommended number of households per PSU (in this case, b=10), n_{d}^{'} is the number of households allocated to domain d (Table 5, last column).

(2) Compute the sampling interval:

(7)   \begin{equation*} \frac{\sum_\alpha M_{h\alpha }}{a_{d}^{'}} = \frac{N_{d}}{a_{d}^{'}}. \end{equation*}

(3) Sort all the PSUs in domain d by zila, urban/rural classification, by strata and lastly, by PStrong values.

(4) Compute the cumulative value of the measure of size (total number of households based from 2001 Census of Population), M_{h\alpha} using the sorted list in step (3).

(5) Select a random start (RS) by drawing a random number between 0 and 1 and multiplying it by the interval in step 2. The first sampled PSU will be the first PSU with cumulative value of M_{h\alpha} containing the value of the random start (RS). The next sample PSU will be the PSU for which the cumulative value of M_{h\alpha} contains RS + S_d, the next will be the PSU for which the cumulative value contains RS + 2 * S_d, etc.

Table 7. Summary of Sample Statistics by Domain

Division Total No. of HouseholdsN_d Computed Sample PSUsa_{d}^{'} Sampling IntervalS_d Actual Number of sample PSUsa_d Tentative Sample Householdshat{n}_d Selection Probabilityf_d
Barisal 1,648,085 181.77 9066.992 182 1820 0.001104
Chittagong 4,472,548 246.05 18177.35 246 2460 0.000550
Dhaka 8,236,687 369.66 22282.06 370 3700 0.000449
Khulna 3,119,602 210.24 14838.39 210 2100 0.000673
Rajshahi 6,627,797 314.01 21107.21 314 3140 0.000474
Sylhet 1,388,222 178.28 7786.691 178 1780 0.001282

Source: Authors’ computations using data from 2001 Census of Population conducted by BBS.

Sample Selection of Households

Since the measure of size (i.e., total number of households) that was used for selecting the PSUs is based on 2001 Census of Population which is quite far from the 2009-2010 reference period of the LFS, the number of households to be sampled must be adjusted accordingly to maintain the uniform selection probabilities within domain. In particular, since the households will be selected from a sampled PSU \alpha with P(h\beta|\alpha)=\frac{b_h}{M_{h\alpha}} and if the 2009-2010 value of the measure of size is denoted as N_{h\alpha}, then maintaining the same household level selection probability means that

(8)   \begin{equation*} P(h\beta|\alpha) = \frac{b_{h}}{M_{h\alpha}}=\frac{10}{M_{h\alpha}}=\frac{b_{h\alpha}^{'}}{N_{h\alpha}}, \end{equation*}

and hence,

(9)   \begin{equation*} b_{h\alpha}^{'} = \frac{N_{h\alpha}}{M_{h\alpha}}*10, \end{equation*}

where b_{h\alpha}^{'} is the actual total number of households to be selected in PSU \alpha in stratum h. This implies that the there should be a listing operation of all households in the selected PSUs before the conduct of the 2009-2010 LFS.

6. Survey Weights and Estimation

The complex design of the master sample has to be considered in analyzing the 2009-2010 LFS and other surveys that will use the master sample in the future. Survey weights must be used to produce estimates of population parameters and design features such as the stratification measures, PSUs and domains must be taken into account in variance estimation and inference.

6.1 Survey Weights

The final survey weights are the product of at most three successive stages of computations. First, base weights are computed to counteract the unequal selection probabilities in the sample design. Then the base weights are adjusted to balance uneven response rates and if data are available, the non-response adjusted weights are further adjusted to ensure that the weighted sample distributions conform with known distributions from valid auxiliary data sources.

The base weight for sampled household is the inverse of its selection probability. In the master sample design, the selection probability is uniform within a domain and hence, base weights will not also vary within domains. In general,

(10)   \begin{equation*} w_{d}^{0} = \frac{1}{f_{d}}. \end{equation*}

Table 8 presents the base weights of sampled households by division.

Table 8. Base Weights by Domain

Division Selection Probabilityf_d Base Weightw^0_d
Barisal 0.001104 905.7971
Chittagong 0.000550 1818.1820
Dhaka 0.000449 2227.1710
Khulna 0.000673 1485.8840
Rajshahi 0.000474 2109.7050
Sylhet 0.001282 780.0312

Source: Authors’ computations using data from 2001 Census of Population conducted by BBS

Non-response adjustments will have to be incorporated in the final survey weights if the degree of unit non-response cannot be ignored. Unit non-response occurs when an eligible household fails to participate in the survey. For example, households may refuse to participate or an eligible respondent may not be available at the times that the survey interviewer visits. In general, the non-response adjustment inflates the base weights of “similar” responding units to compensate for the non-respondents. The most common form of non-response weighting adjustment is a weighting class type. The full sample of respondents and non-respondents is divided into a number of weighting classes or cells and non-response adjustment factors are computed for each cell c (Kalton, 1990) as

(11)   \begin{equation*} w_{c}^{1} = \frac{\sum_{i\epsilon rc} w_{di} +\sum_{j\epsilon mc} w_{dj}}{\sum_{i\epsilon rc}^{.}w_{di}} = \frac{\sum_{i\epsilon sc} w_{di}}{\sum_{i\epsilon rc} w_{di}}, \end{equation*}

where the denominator of w_c^1 is the sum of the weights of respondents (indexed r) in weighting cell c while the numerator adds together the sum of the weights for respondents and the sum of the weights for eligible non-respondents (indexed m for missing) in cell c which is equal to the sum of the weights for the total eligible sample (indexed s) in cell c. Thus, the non-response weight adjustment w_c^1 is the inverse of the weighted response rate in cell c. Note that the adjustment is applied with eligible units. Ineligible sampled units (e.g., vacant or demolished housing units and units out of scope for a given survey) are excluded.

Weighting cells c need not conform with the strata boundaries. They may cut across strata but it is important that the weighting cells will capture “similar” households. Similarity is viewed here in the perspective of the households propensity to response. In general, the response rates across weighting cells will vary widely. Moreover, there may be instances that the weighted sample distributions will not conform with projected population counts. When this happens, further weighting adjustments or what is known as population weighting adjustments can be incorporated in the final survey weight to ensure that the sample distribution conforms with the population distribution. Population weighting adjustment is performed similar to the non-response weighting adjustments described earlier. Calibration methods such as raking are used in this process. Using an iterative proportional fitting algorithm, raking is performed on the non-response adjusted weights such that the weighted survey estimates of some characteristics of interest (e.g. age group and sex) conform with the corresponding population distributions.

6.2 Estimation

Assuming that the final survey weight for household i is w_i or what can be viewed as the number of population units that the responding household i represent. Then the estimator of a population total for characteristic of interest Y will be \hat{Y} = \sum_{i\epsilon s} w_{i}y_{i}, where y_{i} is the value of the variable y for household i.

The simple estimator \hat{Y} has many applications. For example, it can be applied to estimate the count of population with specific characteristic of interest, by setting y_i=1 if household i has the specific characteristic, 0 otherwise.

To estimate the population mean, \bar{Y}, the following ratio estimator can be used:

(12)   \begin{equation*} \bar{y} = \frac{\sum_{i\epsilon s} w_{i}y_{i}}{\sum_{i\epsilon s} w_{i}}, \end{equation*}

with the total of the survey weights of all responding households, \sum_{i \in s}w_i, as an estimator for the total number of households. A more general form of the ratio estimator (Kalton, 1983) would be:

(13)   \begin{equation*} R = \frac{\sum_{i\epsilon s} w_{i}y_{i}}{\sum_{i\epsilon s} w_{i}x_{i}}. \end{equation*}

Note that with complex sample design such as the master sample, the means depicted in (12) and (13) are ratio estimators that involve the ratio of two random variables and hence, must be carefully considered in the computation of sampling errors.

6.3 Variance Estimation

 

The variances of survey estimates are needed to evaluate the precision of the survey.  The sampling design in addition to the sample size is critical to the precision of survey estimates. The statistical software packages have modules that can approximate the variance of estimates from complex surveys.  Most of these software packages make use of the Taylor series approach in computing the variance, although some software also offers alternate approach in the form of replication, resampling or bootstrap procedures. In general, each variance estimation approach has its own advantages and limitations. For instance, while Taylor series expansion approach is more straightforward to implement, incorporating non-response adjustments may render this technique less appropriate. In such context, resampling procedures may give more accurate approximations of the true variance.  Nevertheless, in all these variance estimation techniques, specifying the features of the survey design is required.  Also, these approaches involve approximations, most are anchored on the assumption that the first stage sampling fractions are small.

 

Note that survey estimates at the (geographic) division level are expected to have sampling error at acceptable level. This is also expected for estimates at the national level that cut across domains. For example, unemployment rates at urban/rural area levels are expected to have tolerable sampling errors. It is important that sampling errors of major estimates should be derived to validate these expectations. Moreover, sampling errors are also needed to evaluate the reliability of estimates at the sub-division level (e.g., zila level in the case of Bangladesh). Estimates for sub-division with sufficient sample size may render acceptable sampling errors. In the case of Bangladesh, some zilas still have relatively large sample size. Thus, although the divisions are set as the design domains or explicit strata, some estimates at the zila level may still have tolerable sampling error. However, disaggregating zila-level estimates by urban/rural may not at all be possible because of insufficient sample size.

7. Summary

The paper documents the technical processes that were undertaken in the development of the new sample design that was used for the 2009-2010 Labor Force Survey conducted in Bangladesh. The new sample design addresses the weaknesses identified in the previous design adopted in 2005 LFS. Some of the (proposed) changes are as follows: first, considering the positive intra class correlations of major characteristics of interest, the total number of households to be enumerated per was reduce from 40 to 10 while the number of PSUs to be selected was increased from 1000 to 1500.  Second, effective sample allocation procedure was implemented to ensure the reliability of estimates at the division-level as well as those that cut across divisions. Third, implicit stratification measures were introduced to reduce design effects. Fourth, a sample selection procedure that maintains uniform selection probability for each division was also adopted to counter the large design effects noted from 2005 LFS.

Appendix 1

The Integrated Multi-Purpose Sample Design

The Integrated Multi-Purpose Sample Design (IMPS) was used by the Bangladesh Bureau of Statistics (BBS) to sample households for surveys of national coverage. Two such surveys are the 2005-06 Labour Force Survey (LFS) and the 2005 Household Income and Expenditure Survey. In general, IMPS has a stratified cluster design. Clusters of about 200 households each were formed as enumeration blocks for each zila (municipality) on the basis of the 2001 Census of Population. These enumeration blocks served as the primary sampling units (PSUs) in IMPS and were classified as urban, rural and statistical metropolitan areas (SMA). Further geographical stratification were also introduced by classifying the zilas according to six divisions – Barisabal, Chittagong, Dhaka, Khulna, Rajshahi and Sylhet. In all, there were 129 strata formed – 64 strata corresponding to 64 rural zilas, 61 strata classified under urban with the other three, Gazipur, Narayanganj and Khulna taken together to form one strata under SMA in addition to the other three SMA strata formed from urban areas with very large population – Dhaka, Chittagong, Rajshahi.

Of the 109,000 (?) PSUs, 1000 were selected. The procedure for allocating the PSUs to the 129 strata was not clarified in the documentation. Appendix 1 presents the distribution of the PSUs to the strata. Moreover, the procedure for selecting the PSUs was not also included in the documentation. For each selected PSUs, 40 households were selected at random making the total sample households equal to 40,000.

The survey weight usually derived as the product of the base weight (equal to the inverse of the selection probability) and the adjustments for non-response and non-coverage, was not determined as such. Instead, the survey weight was derived as the ratio of total households in the strata (updated as of April 2006) to the sample households. Appendix 2 presents the survey weights that were derived.
Summary of PSU Allocation Across Strata

Strata National Rural Urban SMA
Barisal Division 80 55 25 -
06- Barisal zila 17 12 5 -
09- Bhola zila 14 10 4 -
42- Jhalokati zila 12 8 4 -
79- Perojpur zila 12 8 4 -
04- Barguna zila 12 8 4 -
78- Patuakhali zila 13 9 4 -
Chittagong Division 179 116 49 14
03- Bandarban zila 12 8 4 -
15- Chittagong zila 34 16 4 14
22- Cox’s Bazar zila 12 8 4 -
12- Brahmanbaria zila 15 10 5 -
13- Chandpur zila 15 10 5 -
19- Comilla zila 26 20 6 -
46- Khagrachhari zila 12 8 4 -
30- Feni zila 12 8 4 -
51- Lakshmipur zila                                               12 8 4 -
75- Noakhali zila 17 12 5 -
84- Rangamati zila 12 8 4 -
Dhaka division 289 172 73 44
26- Dhaka zila 34 8 4 22
33- Gazipur zila 18 8 - 10
56- Manikganj zila 12 8 4 -
59- Munshiganj zila 12 8 4 -
67- Narayanganj zila 20 8 - 12
68- Narshingdi zila 15 9 6 -
29- Faridpur zila 14 10 4 -
35- Gopalganj zila 12 8 4 -
54- Madaripur zila 12 8 4 -
82- Rajbari zila 12 8 4 -
86- Shariatpur zila 12 8 4 -
39- Jamalpur zila 15 10 5 -
89- Sherpur zila 13 9 4 -
48- Kishoreganj zila 17 12 5 -
61- Mymensingh zila 33 23 10 -
72- Netrokona zila 14 10 4 -
93- Tangail zila 24 17 7 -
Khulna division 146 89 45 12
41- Jessore zila 20 12 8 -
44- Jhenaidah zila 15 9 6 -
55- Magura zila 12 8 4 -
65- Narail zila 12 8 4 -
01- Bagerhat zila 13 8 5 -
47- Khulna zila 20 8 - 12
87- Satkhira zila 14 10 4 -
18- Chuadanga zila 13 8 5 -
50- Kushtia zila 15 10 5 -
57- Meherpur zila 12 8 4 -
Rajshahi division 251 170 71 10
10- Bogra zila 21 16 5 -
38- Joypurhat zila 12 8 4 -
27- Dinajpur zila 18 13 5 -
77- Panchagar zila 12 8 4 -
94- Thakurgaon zila 12 8 4 -
76- Pabna zila 16 10 6 -
88- Sirajganj zila 18 13 5 -
64- Naogaon zila 17 13 4 -
69- Natore zila 14 10 4 -
70- Nowabganj zila 12 8 4 -
81- Rajshahi zila 24 10 4 10
32- Gaibandha zila 16 12 4 -
49- Kurigram zila 15 10 5 -
52- Lalmonirhat zila 12 8 4 -
73- Nilphamari zila 13 9 4 -
85- Rangpur zila 19 14 5 -
Sylhet division 55 38 17 -
36- Hobiganj zila 13 9 4 -
58- Maulvibazar zila 13 9 4 -
90- Sunamganj zila 14 10 4 -
91- Sylhet zila 15 10 5 -
Total 1000 640 280 80

Appendix 2

Integrated Multi Purpose Sampling Design

Survey Weights by Stratum

Stratum Total updated households Sample households Sampling weights
Rural Urban SMA Rural Urban SMA Rural Urban SMA
06 Barisal 442170 94384 0 480 200 921.19 471.92 0.00
09 Bhola 327262 61052 0 400 160 818.15 381.58 0.00
42 Jhalokati 130186 27988 0 320 160 406.83 174.92 0.00
79 Perojpur 208895 42063 0 320 160 652.80 262.89 0.00
04 Barguna 169695 22626 0 320 160 530.30 141.42 0.00
78 Patuakhali 303056 29761 0 360 160 841.82 186.00 0.00
03 Bandarban 47290 18186 0 320 160 147.78 113.66 0.00
15 Chittagong 749021 19916 840746 640 120 600 1170.34 165.97 1401.24
22 Cox’s Bazar 347072 45420 0 320 160 1084.60 283.87 0.00
12 Brahmanbaria 469347 61421 0 400 200 1173.37 307.11 0.00
13 Chandpur 439039 61017 0 400 200 1097.60 305.08 0.00
19 Comilla 933277 95049 0 800 240 1166.59 396.04 0.00
46 Khagrachhari 80753 31643 0 320 160 252.35 197.77 0.00
30 Feni 235576 33292 0 320 160 736.17 208.08 0.00
51 Lakshmipur 286643 44258 0 320 160 895.76 276.61 0.00
75 Noakhali 520274 55253 0 480 200 1083.91 276.27 0.00
84 Rangamati 79856 34145 0 320 160 249.55 213.41 0.00
26 Dhaka 167198 3491 2191848 320 160 880 522.50 21.82 2490.74
33 Gazipur 257960 0 247896 320 0 400 806.13 0.00 619.74
56 Manikganj 274091 21605 0 320 160 856.53 135.03 0.00
59 Munshiganj 255236 37078 0 320 160 797.61 231.73 0.00
67 Narayanganj 222924 0 331883 320 0 480 696.64 0.00 691.42
68 Narshingdi 350319 80406 0 360 240 973.11 335.03 0.00
29 Faridpur 346816 48608 0 400 160 867.04 303.80 0.00
35 Gopalganj 237833 23708 0 320 160 743.23 148.18 0.00
54 Madaripur 225717 30776 0 320 160 705.36 192.36 0.00
82 Rajbari 190272 25943 0 320 160 594.59 162.15 0.00
86 Shariatpur 223253 22255 0 320 160 697.66 139.09 0.00
39 Jamalpur 397902 79792 0 400 200 994.76 398.96 0.00
89 Sherpur 255789 31996 0 360 160 710.53 199.98 0.00
48 Kishoreganj 505921 74145 0 480 200 1054.00 370.73 0.00
61 Mymensingh 875150 136206 0 920 400 951.25 340.52 0.00
72 Netrokona 406897 40560 0 400 160 1017.25 253.50 0.00
93 Tangail 646284 93884 0 680 280 950.42 335.30 0.00
41 Jessore 470209 99110 0 480 320 979.60 309.72 0.00
44 Jhenaidah 314635 46953 0 360 240 873.98 195.63 0.00
55 Magura 167265 22115 0 320 160 522.70 138.22 0.00
65 Narail 144385 15628 0 320 160 451.20 97.67 0.00
01 Bagerhat 293772 55545 0 320 200 918.04 277.72 0.00
47 khulna 255885 0 327109 320 0 480 799.64 0.00 681.47
87 Satkhira 394005 30802 0 400 160 985.02 192.51 0.00
18 Chuadanga 170231 61525 0 320 200 531.97 307.63 0.00
50 Kushtia 360554 39471 0 400 200 901.39 197.35 0.00
57 Meherpur 120478 14850 0 320 160 376.49 92.82 0.00
10 Bogra 603687 93314 0 640 200 943.26 466.57 0.00
38 Joypurhat 179002 18762 0 320 160 559.38 117.26 0.00
27 Dinajpur 526401 84258 0 520 200 1012.31 421.30 0.00
77 Panchagar 172454 20929 0 320 160 538.92 130.81 0.00
94 Thakurgaon 257353 22835 0 320 160 804.22 142.72 0.00
76 Pabna 389278 112917 0 400 240 973.19 470.49 0.00
88 Sirajganj 549959 67454 0 520 200 1057.61 337.27 0.00
64 Nogaon 503878 46560 0 520 160 969.00 290.99 0.00
69 Natore 300966 49842 0 400 160 752.41 311.51 0.00
70 Nawabganj 252512 77584 0 320 160 789.10 484.90 0.00
81 Rajshahi 347804 26871 166673 400 160 400 869.51 167.94 416.68
32 Gaibandha 448228 43073 0 480 160 933.81 269.21 0.00
49 Kurigram 347381 59961 0 400 200 868.46 299.81 0.00
52 Lalmonirhat 222298 32851 0 320 160 694.68 205.32 0.00
73 Nilphamari 314999 46125 0 360 160 874.99 288.29 0.00
85 Rangpur 489418 95717 0 560 200 873.96 478.59 0.00
36 Habiganj 359402 47883 0 360 160 998.34 299.27 0.00
58 Maulvibazar 339274 34324 0 360 160 942.43 214.53 0.00
90 Sunamganj 413830 48966 0 400 160 1034.58 306.03 0.00
91 Sylhet 482356 114533 0 400 200 1205.90 572.67 0.00

2009 Master Sample

PSU Count by Division, Zila and Urban/Rural Classification

Division Zila Rural Urban Total
1 2 3 4 1 2
Barisal Barguna 231 386 497 541 214 1869
Barisal 1328 1046 841 780 314 511 4820
Bhola 434 604 824 1034 313 170 3379
Jhaloka 425 392 227 116 105 96 1361
Patuakh 553 613 662 679 173 175 2855
Pirojpu 599 525 521 422 184 159 2410
Chittagong Bandarb 236 421 253 910
Brahman 498 763 1074 1171 340 231 4077
Chandpu 738 1160 1084 704 605 4291
Chittagong 2344 1358 1126 702 2321 4306 12157
Comilla 1203 2032 2428 1712 518 466 8359
Cox’s B 460 481 698 828 444 2911
Feni 870 579 445 285 2179
Khagrac 364 669 452 1485
Lakshmi 577 693 547 654 424 2895
Noakhal 1476 1133 734 828 706 4877
Rangama 311 620 459 1390
Dhaka Dhaka 756 274 366 5530 10919 17845
Faridpu 693 762 789 779 450 3473
Gazipur 698 629 505 384 1099 577 3892
Gopalga 429 539 474 500 204 2146
Jamalpu 447 989 1229 1347 761 4773
Kishorg 988 1252 1170 1281 759 5450
Madarip 412 515 497 556 270 2250
Manikga 793 753 620 471 213 2850
Munshig 1234 520 335 265 2354
Mymensi 993 1920 2371 2402 938 358 8982
Narayan 1443 302 1367 899 4011
Narsing 1372 867 524 313 658 3734
Netrako 268 600 1105 1712 378 4063
Rajbari 284 424 499 443 218 1868
Shariat 450 500 519 606 238 2313
Sherpur 297 713 880 750 285 2925
Tangail 1608 1702 1514 1300 931 7055
Khulna Bagerha 932 751 487 389 417 2976
Chuadan 176 328 504 528 317 267 2120
Jessore 926 978 1065 995 279 506 4749
Jhenaid 350 602 721 926 227 223 3049
Khulna 592 500 476 466 1174 1167 4375
Kushtia 1278 738 663 524 186 253 3642
Magura 205 330 367 490 216 1608
Meherpu 448 348 312 150 1258
Narail 310 334 276 273 147 1340
Satkhir 824 840 810 824 138 156 3592
Rajshahi Bogra 1967 1376 1114 999 233 531 6220
Dina 1050 1216 1273 1202 307 460 5508
Gaiba 1109 1490 1154 873 487 5113
Joypu 234 424 486 438 255 1837
Kurig 504 986 967 847 606 3910
Lalmo 272 482 596 711 353 2414
Naoga 578 911 1336 1912 403 5140
Nator 546 615 725 842 413 3141
Nawab 755 533 484 352 520 2644
Nilph 412 688 731 788 225 249 3093
Pabna 1261 702 654 659 449 407 4132
Panch 274 373 486 449 153 1735
Rajshahi 551 802 880 813 717 1009 4772
Rangp 1090 1400 1202 950 556 382 5580
Siraj 2490 997 692 782 685 5646
Thaku 288 376 622 783 214 2283
Sylhet Habigan 400 636 909 1037 264 101 3347
Maulvib 1109 792 607 324 146 153 3131
Sunamga 292 629 1002 1455 290 91 3759
Sylhet 1445 1193 729 433 213 568 4581
Bangladesh 48032 47496 47471 47101 32078 26726 248904

Appendix 4

2009 Master Sample

Sample PSU Count by Division, Zila and Urban/Rural Classification

Division Zila Rural Urban Total
1 2 3 4 1 2
Barisal Barguna 3 4 5 6 2 20
Barisal 15 11 9 8 4 5 52
Bhola 5 6 9 11 4 1 36
Jhaloka 5 5 3 1 1 1 16
Patuakh 7 7 7 7 2 2 32
Pirojpu 7 5 6 4 2 2 26
Chittagong Bandarb 1 1 1 3
Brahman 3 5 6 7 2 1 24
Chandpu 4 7 6 3 4 24
Chittagong 13 8 7 4 13 23 68
Comilla 7 11 13 9 3 3 46
Cox’s B 2 3 4 4 3 16
Feni 5 3 3 1 12
Khagrac 2 2 2 6
Lakshmi 3 4 3 4 2 16
Noakhal 8 6 4 4 3 25
Rangama 2 2 2 6
Dhaka Dhaka 4 1 2 24 50 81
Faridpu 3 3 4 3 2 15
Gazipur 4 3 2 2 6 3 20
Gopalga 3 2 2 2 1 10
Jamalpu 2 5 6 6 3 22
Kishorg 5 5 5 6 3 24
Madarip 2 2 3 2 1 10
Manikga 4 3 3 2 1 13
Munshig 6 2 2 1 11
Mymensi 5 9 12 11 5 1 43
Narayan 8 1 7 5 21
Narsing 6 4 2 2 3 17
Netrako 1 3 5 8 2 19
Rajbari 1 2 2 2 1 8
Shariat 2 2 2 3 1 10
Sherpur 1 3 4 4 1 13
Tangail 8 8 7 5 5 33
Khulna Bagerha 7 6 3 3 3 22
Chuadan 1 3 3 4 2 2 15
Jessore 7 8 8 7 2 3 35
Jhenaid 3 4 6 7 1 2 23
Khulna 4 4 4 3 9 10 34
Kushtia 8 6 4 4 1 2 25
Magura 2 2 2 4 1 11
Meherpu 3 3 2 1 9
Narail 3 2 2 2 1 10
Satkhir 6 6 6 6 1 1 26
Rajshahi Bogra 11

References

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3. Kish, L. (1965) Survey Sampling , New York: Wiley

4. Kish, L. (1987) Statistical Design for Research, New York: Wiley

5. Kozak, M. (2004). Optimal stratification using random search method in agricultural surveys. Statistics in Transition, 6(5), 797-806.

6. Lohr, S.L. (2010) Sampling: Design and Analysis, Second edition, Boston: Brooks/Cole

7. Sethi, V. K. (1963) A note on optimum stratification of populations for estimating the population means. The Australian Journal of Statistics, 5, 20-33.

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10. http://www.inside-r.org/packages/cran/stratification/docs/strata.LH accessed 11 June, 2013.



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