Note on Sample Design and Estimation Procedure of NSS 71 st Round

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1 of NSS 7 st Roud. Itroductio. The Natioal Sample Survey (NSS), set up by the Govermet of Idia i 950 to collect socioecoomic data employig scietific samplig methods, started its sevety first roud from st Jauary 204 ad will cotiue up to 30 th Jue Subect Coverage: The 7 st roud (Jauary 204 Jue 204) of NSS is devoted to the subect of Social Cosumptio ad earmarked for surveys o Health ad Educatio. The last survey o health was coducted i 60 th roud of NSS (Jauary Jue 2004) ad the same o educatio was coducted durig 64 th roud of NSS (July Jue 2008). 2. Outlie of Survey Programme 2. Geographical coverage: This survey covers the whole of the Idia Uio. 2.2 Period of survey ad work programme: The period of survey is of six moths duratio startig o st Jauary 204 ad edig o 30 th Jue Sub-rouds: The survey period of this roud is divided ito two sub-rouds of three moths duratio each as follows: sub-roud : Jauary - March 204 sub-roud 2 : April - Jue 204 I each of these two sub-rouds equal umber of sample villages/ blocks (FSUs) is allotted for survey with a view to esurig uiform spread of sample FSUs over the etire survey period. Attempt has bee made to survey each of the FSUs durig the sub-roud to which it is allotted. Because of the arduous field coditios, this restrictio is ot strictly eforced i Adama ad Nicobar Islads, Lakshadweep, Leh (Ladakh) ad Kargil districts of Jammu & Kashmir ad rural areas of Aruachal Pradesh ad Nagalad. 2.4 Schedules of equiry: Durig this roud, the followig schedules of equiry are beig cavassed: Schedule 0.0 : List of Households Schedule 25.0 : Schedule 25.2 : Social cosumptio: Health Social cosumptio: Educatio

2 2.5 Participatio of States: I this roud all the States ad Uio Territories except Adama & Nicobar Islads, Chadigarh, Dadra & Nagar Haveli ad Lakshadweep are participatig. The followig is the matchig patter of the participatig States/ UTs. State/UT Nagalad (U) Adhra Pradesh, Jammu & Kashmir, Maipur Maharashtra (U) Remaiig States/ UTs Extet of matchig triple double oe ad half equal 3. Sample Desig 3. Outlie of sample desig: A stratified multi-stage desig has bee adopted for the 7 st roud survey. The first stage uits (FSU) are the cesus villages (Pachayat wards i case of Kerala) i the rural sector ad Urba Frame Survey (UFS) blocks i the urba sector. The ultimate stage uits (USU) are households i both the sectors. I case of large FSUs, oe itermediate stage of samplig is the selectio of two hamlet-groups (hgs)/ sub-blocks (sbs) from each rural/ urba FSU. 3.2 Samplig Frame for First Stage Uits: For the rural sector, the list of 20 cesus villages (heceforth the term village would mea Pachayat wards for Kerala) costitutes the samplig frame. I case of Kerala, due to the o-availability of Pachayat wards based o cesus 20, the available list of Pachayat wards based o cesus 200 is used as the rural frame. For the urba sector, the latest updated list of UFS blocks (phase ) is cosidered as the samplig frame. 3.3 Stratificatio: Stratum has bee formed at district level. Withi each district of a State/UT, geerally speakig, two basic strata have bee formed: (i) rural stratum comprisig of all rural areas of the district ad (ii) urba stratum comprisig of all the urba areas of the district. However, withi the urba areas of a district, if there are oe or more tows with populatio lakh or more as per Cesus 20, each of them formed a separate basic stratum ad the remaiig urba areas of the district has bee cosidered as aother basic stratum Special stratum i the rural sector: There are some villages i Nagalad ad Adama & Nicobar Islads which reamis difficult to access. As i earlier rouds, a special stratum has bee formed at State/UT level comprisig these villages i the two State/UTs. 3.4 Sub-stratificatio: 3.4. Rural sector: If r be the sample size allocated for a rural stratum, the umber of sub-strata formed was r/2. The villages withi a district as per frame have bee first arraged i ascedig order of populatio. The sub-strata to r/2 have bee demarcated i such a way that each substratum comprised a group of villages of the arraged frame ad had more or less equal populatio. A-2

3 3.4.2 Urba sector: If u be the sample size allocated for a urba stratum, the umber of substrata formed was u/2. For all strata, if u/2 >, implyig formatio of 2 or more sub-strata, all the UFS blocks withi the stratum have bee first arraged i ascedig order of total umber of households i the UFS Blocks as per UFS phase The sub-strata to u/2 have bee demarcated i such a way that each sub-stratum had more or less equal umber of households. 3.5 Total sample size (FSUs): 8300 FSUs have bee allocated for the cetral sample at all-idia level. For the state sample, there are 9274 FSUs allocated for all-idia. State wise allocatio of sample FSUs is give i Table. 3.6 Allocatio of total sample to States ad UTs: The total umber of sample FSUs heve bee allocated to the States ad UTs i proportio to populatio as per Cesus 20 subect to a miimum sample allocatio to each State/ UT. While doig so, the resource availability i terms of umber of field ivestigators has bee kept i view. 3.7 Allocatio of State/ UT level sample to rural ad urba sectors: State/UT level sample size has bee allocated betwee two sectors i proportio to populatio as per Cesus 20 with double weightage to urba sector subect to the restrictio that urba sample size for bigger states like Maharashtra, Tamil Nadu etc. do ot exceed the rural sample size. A miimum of 6 FSUs (miimum 8 each for rural ad urba sector separately) is allocated to each State/ UT. 3.8 Allocatio to strata: Withi each sector of a State/ UT, the respective sample size has bee allocated to the differet strata i proportio to the populatio as per Cesus 20. Stratum level allocatio has bee adusted to multiples of 2 with a miimum sample size of 2. For special strata i the rural areas of Nagalad ad A & N Islads, 4 FSUs has bee allocated to each. 3.9 Allocatio to sub-strata: Allocatio for each sub-stratum has bee 2 i both rural ad urba sectors. 3.0 Selectio of FSUs: For the rural sector, from each stratum/sub-stratum, required umber of sample villages have bee selected by Probability Proportioal to Size With Replacemet (PPSWR), size beig the populatio of the village as per Cesus 20. For the urba sector, from each stratum/sub-stratum, FSUs have bee selected by Probability Proportioal to Size With Replacemet (PPSWR), size beig the umber of households of the UFS Blocks. Both rural ad urba samples have bee draw i the form of two idepedet sub-samples ad equal umber of samples has bee allocated amog the two sub rouds. A-3

4 3. Selectio of hamlet-groups/ sub-blocks - importat steps 3.. Criterio for hamlet-group/ sub-block formatio: After idetificatio of the boudaries of the FSU, it is to be determied whether listig will be doe i the whole sample FSU or ot. I case the approximate preset populatio of the selected FSU is foud to be 200 or more, it will be divided ito a suitable umber (say, D) of hamlet-groups i the rural sector ad sub-blocks i the urba sector by more or less equalisig the populatio as stated below. approximate preset populatio of the sample FSU o. of hg s/sb s to be formed less tha 200 (o hamlet-groups/sub-blocks) 200 to to to to ad so o - For rural areas of Himachal Pradesh, Sikkim, Uttarakhad (except four districts Dehradu, Naiital, Hardwar ad Udham Sigh Nagar), Pooch, Raouri, Udhampur, Reasi, Doda, Kistwar, Ramba, Leh (Ladakh), Kargil districts of Jammu ad Kashmir ad Idukki district of Kerala, the umber of hamlet-groups will be formed as follows: approximate preset populatio of the sample village o. of hg s to be formed less tha 600 (o hamlet-groups) 600 to to to to ad so o Formatio ad selectio of hamlet-groups/ sub-blocks: I case hamlet-groups/ sub-blocks are to be formed i the sample FSU, the same should be doe by more or less equalizig populatio. Note that while doig so, it is to be esured that the hamlet-groups/ sub-blocks formed are clearly idetifiable i terms of physical ladmarks. Two hamlet-groups (hg)/ sub-blocks (sb) will be selected from a large FSU wherever hamletgroups/ sub-blocks have bee formed i the followig maer oe hg/ sb with maximum percetage share of populatio will always be selected ad termed as hg/ sb ; oe more hg/ sb will be selected from the remaiig hg s/ sb s by simple radom samplig (SRS) ad termed as hg/ sb 2. Listig ad selectio of the households will be doe idepedetly i the two selected hamletgroups/ sub-blocks. The FSUs without hg/ sb formatio will be treated as sample hg/ sb umber. A-4

5 3.2 Formatio of secod stage strata ad allocatio of households: SSS compositio of SSS withi a sample FSU Schedule 25.0: Social Cosumptio: Health SSS SSS 2 households havig at least oe child of age less tha year from the remaiig, households with at least oe member (icludig deceased former member) hospitalised durig last 365 days umber of households to be surveyed FSU with hg/sb FSU without formatio hg/sb formatio (for each hg/sb) SSS 3 other households 2 Schedule 25.2: Social Cosumptio: Educatio SSS SSS 2 SSS 3 households with at least oe studet receivig techical/professioal educatio from the remaiig, households havig at least oe studet receivig geeral educatio other households Selectio of households: From each SSS, for both the schedules, the sample households are selected by SRSWOR. A-5

6 4. Estimatio Procedure 4. Notatios: s = subscript for s-th stratum t = subscript for t-th sub-stratum m = subscript for sub-sample (m =, 2) i = subscript for i-th FSU [village (pachayat ward)/ block] d = subscript for a hamlet-group/ sub-block (d =, 2) = subscript for -th secod stage stratum i a FSU/ hg/sb [ =, 2 or 3] k = subscript for k-th sample household uder a particular secod stage stratum withi a FSU/ hg/sb D = total umber of hg s/ sb s formed i the sample FSU D* = 0 if D = = (D ) for FSUs with D > = total size of a rural/urba sub-stratum (= sum of sizes for all the FSUs of a sub-stratum) z = size of sample village/ufs block used for selectio. = umber of sample FSUs surveyed icludig uihabitated ad zero cases but excludig casualty for a particular sub-sample ad sub-stratum. H = total umber of households listed i a secod-stage stratum of a FSU / hamlet-group or subblock of sample FSU h = umber of households surveyed i a secod-stage stratum of a FSU / hamlet-group or subblock of sample FSU x, y = observed value of characteristics x, y uder estimatio Xˆ, = estimate of populatio total X, Y for the characteristics x, y Uder the above symbols, y stmidk = observed value of the characteristic y for the k-th household i the -th secod stage stratum of the d-th hg/ sb (d =, 2) of the i-th FSU belogig to the m-th sub-sample for the t-th sub-stratum of s-th stratum. However, for ease of uderstadig, a few symbols have bee suppressed i followig paragraphs where they are obvious. A-6

7 4.2 Formulae for Estimatio of Aggregates for a particular sub-sample ad stratum substratum: 4.2. Schedule 0.0: Rural/Urba: (i) For estimatig the umber of households i a stratum sub-stratum possessig a characteristic: = i = z i * [ y + D y ] i i i 2 where y i, y i 2 are the total umber of households possessig the characteristic y i hg s & 2 of the i-th FSU respectively. (ii) For estimatig the umber of villages i a stratum sub-stratum possessig a characteristic: where = y i i = z i y i is take as for sample villages possessig the characteristic ad 0 otherwise Schedules 25.0 & 25.2: Rural/ Urba: (i) For -th secod-stage stratum of a stratum sub-stratum: = h i hi 2 i * i 2 y i k + D i i = z i hi k hi 2 k = H H = y i 2 k (ii) For all secod-stage strata combied: = ˆ Y A-7

8 4.3 Overall Estimate for Aggregates for a sub-stratum: Overall estimate for aggregates for a sub-stratum ( Ŷ st ) based o two sub-samples i a sub-stratum is obtaied as: 2 = ˆ st Y stm 2 m = 4.4 Overall Estimate for Aggregates for a stratum: Overall estimate for a stratum ( s ) will be obtaied as = ˆ s Y st t 4.5 Overall Estimate of Aggregates at State/UT/all-Idia level: The overall estimate at the State/ UT/ all-idia level is obtaied by summig the stratum estimates Ŷs over all strata belogig to the State/ UT/ all-idia. 4.6 Estimates of Ratios: Let ad Xˆ be the overall estimates of the aggregates Y ad X for two characteristics y ad x respectively at the State/ UT/ all-idia level. The the combied ratio estimate ˆ Y (R ) of the ratio ( R = ) will be obtaied as X 4.7 Estimates of Error: The estimated variaces of the above estimates will be as follows: 4.7. For aggregate : ( ) ( ) 2 ˆ ˆ) ˆ ˆ ˆ where ar ˆ ( st) = Var ˆ ( Ys) = V ar( Y Var( Yst) s s t Rˆ =. Xˆ V is give by Varˆ st = st st 2, where Y ˆst ad Y ˆst 2 are the estimates for sub-sample ad subsample 2 respectively for stratum s ad sub-stratum 4 t For ratio Rˆ : 2 2 SE ˆ 2 ( Rˆ ) = ( ) + Rˆ ( Xˆ Xˆ ) 2Rˆ ( )( Xˆ Xˆ ) M 2 st st2 st st 2 st st 2 st st2 4Xˆ s t A-8

9 4.7.3 Estimates of Relative Stadard Error (RSE): ( ) V aˆ r R Sˆ E ( ) = Multipliers: ( Rˆ ) M SE ˆ RSE ˆ ( Rˆ ) = 00 Rˆ The formulae for multipliers at stratum/sub-stratum/secod-stage stratum level for a subsample ad schedule type are give below: sch type sector 0.0 rural/urba 25.0/ 25.2 rural/urba st stm formula for multipliers hg / sb hg / sb 2 st z stm stmi H st stm z stmi D * stmi stmi st * stmi 2 Dstmi zstmi hstmi stm zstmi hstmi 2 ( =, 2, 3) H Note: (i) For estimatig ay characteristic for ay domai ot specifically cosidered i sample desig, idicator variable may be used. (ii) Multipliers have to be computed o the basis of iformatio available i the listig schedule irrespective of ay misclassificatio observed betwee the listig schedule ad detailed equiry schedule. * (iii) For estimatig umber of villages possessig a characteristic, D = 0 i the relevat multipliers ad there will be oly oe multiplier for the village. 6. Treatmet for zero cases, casualty cases etc.: 6. While coutig the umber of FSUs surveyed ( sm or stm ) i a stratum/sub-stratum, all the FSUs with survey codes to 6 i schedule 0.0 will be cosidered. I additio, if o SSU is available i the frame for a particular schedule the also that FSU will be treated as surveyed i respect of that schedule. However, if the SSUs of a particular schedule type are available i the frame of the FSU but oe of these could be surveyed the that FSU has to be treated as casualty ad it will ot be treated as surveyed i respect of that schedule. stmi A-9

10 6.2 Casualty cases: FSUs with survey code 7 as per schedule 0.0 are treated as casualties. I additio to this, a FSU, although surveyed, may have to be treated as casualty for a particular schedule type ad a particular secod stage stratum as give i the followig para: 6.2. FSUs with survey codes or 4 as per schedule 0.0 havig umber of households i the frame of -th secod stage stratum greater tha 0 but umber of households surveyed accordig to data file, cosiderig both hg/sb together, as il (i.e. H i + H i2 >0 but h i + h i2 =0) will be take as casualties for -th secod stage stratum. All the FSUs with survey codes to 6 as per schedule 0.0 mius the umber of casualties as idetified above will be take as the umber of surveyed FSUs ( stm ) for that (stratum/sub-stratum) ( secod stage stratum). Whe casualty for -th secod stage stratum occurs for a particular hg/sb but ot for the other hg/sb, the FSU will ot be treated as casualty but some adustmets i the value of H for the other hg/sb will be doe as follows: (i) Suppose for hg/sb, H i > 0 but h i = 0 while for hg/sb 2, H i2 > 0 ad h i2 > 0. I that case * * will be replaced by H + D H ) i the formula for multiplier of hg/sb 2. Di H i 2 ( i i i 2 (ii) Suppose for hg/sb, H i >0 ad h i > 0 while for hg/sb 2, H i2 >0 but h i2 =0. I that case * will be replaced by H + D H ) i the formula for multiplier of hg/sb. ( i i i 2 It may be oted that sm or stm would be same for hg/sb & 2 of a FSU. H i 7. Treatmet i cases of void secod-stage strata/sub-strata /strata at FSU or household level 7. A stratum/sub-stratum may be void because of the casualty of all the FSUs belogig to the stratum/sub-stratum. This may occur i oe sub-sample or i both the sub-samples. If it relates to oly oe sub-sample, the estimate for the void stratum/sub-stratum may be replaced with the estimate as obtaied from the other sub-sample for the same stratum/sub-stratum. 7.2 Whe a stratum/sub-stratum is void i both the sub-samples, the followig procedure is recommeded: Case(I): Stratum/Sub-stratum void cases at FSU levels (i.e. all FSUs havig survey code 7): (i) (ii) If a rural/urba sub-stratum is void the it may be merged with the other sub-stratum of the stratum. If a rural/urba stratum (district) is void due to all FSUs beig casualty, it may be excluded from the coverage of the survey. The state level estimates will be based o the estimates of districts for which estimates are available ad remarks to that effect may be added i appropriate places. A-0

11 Case (II): Stratum/Sub-stratum void case at secod stage stratum level (i.e. all the FSUs are casualties for a particular secod stage stratum): A FSU may be a casualty for a particular secod stage stratum although survey code is ot 7. If all the FSUs of a stratum/sub-stratum become casualties i this maer for a particular secod stage stratum, the stratum/sub-stratum will become void. I such cases, sub-strata will be merged with other sub-strata for all the secod stage strata as i Case (I) above. However, if whole district/stratum becomes void i this maer for a particular secod stage stratum, adustmet for this type of stratum void case may be doe accordig to the followig guidelies. The adustmet will be made ivolvig other strata/sub-strata (withi NSS regio) of the State/U.T. Suppose A, B, C ad D are the four strata i the State/UT/Regio ad stratum C is void for -th secod stage stratum. If a, b ad d are the aggregate estimates for the strata/sub-strata A, B ad D respectively, the the estimate a a + b + b + d + d c c for stratum/sub-stratum C may be obtaied as where a, b, c ad d are the sizes of strata A, B, C ad D respectively. 8. Referece to the values of st, st, s, z sti, D sti, D* sti, D si, D* si, H sti, h sti, H sti2, h sti2: (a) Values of st ad allotted st for the whole roud are give i appedix Table 2 for rural sector ad i Table 3 for urba sector. (b) st should ot be take from the tables. The value of stm for each sub-sample is to be obtaied followig the guidelies give i para 6 above. It icludes uihibited ad zero cases but excludes casualty cases. (c) The value of z sti for the samples selected by PPS is to be take from the colum of sample list uder the headig frame populatio for rural samples ad block size i.e. total umber of households i each UFS block for urba samples. (d) Value of D sti is to be take from item 6 of block, sch 0.0. D* sti is to be calculated from the value of D sti. (e) Values of H sti, H sti2 are to be take from col.(5), block 6 of sch 0.0 for respective hg/sb ad secod-stage stratum. (f) The value of h sti ad h sti2 should ot be take from col (9), block 6 of sch.0.0. The figures should be obtaied by coutig the umber of households i the data file excludig the casualty households. ******** A-

CHAPTER 8 Estimating with Confidence

CHAPTER 8 Estimating with Confidence CHAPTER 8 Estimatig with Cofidece 8.2 Estimatig a Populatio Proportio The Practice of Statistics, 5th Editio Stares, Tabor, Yates, Moore Bedford Freema Worth Publishers Estimatig a Populatio Proportio