OVERVIEW OF SAMPLING SCHEMES

Transcription

1 OVERVIEW OF SAMPLIG SCHEMES Yogta Gharde I.A.S.R.I., ew Delh Itroducto The eed to gather formato arses almost every cocevable sphere of huma actvty. May of the questos that are subject to commo coservato ad cotroversy requre umercal data for ther resoluto. The data collected ad aalyzed a objectve maer ad preseted sutably serve as bass for takg polcy decsos dfferet felds of daly lfe. The mportat users of statstcal data, amog others, clude govermet, dustry, busess, research sttutos, publc orgazatos ad teratoal ageces ad orgazatos. To dscharge ts varous resposbltes, the govermet eeds varety of formato regardg dfferet sectors of ecoomy, trade, dustral producto, health ad mortalty, populato, lvestock, agrculture, forestry, evromet ad avalable resources. The fereces draw from the data help determg future eeds of the ato ad also tacklg socal ad ecoomc problems of people. For stace, the formato o cost of lvg for dfferet categores of people, lvg varous parts of the coutry s of mportace shapg ts polces respect of wages ad prce levels. Data o agrcultural producto are of mmese use to the state for plag to feed the ato. I case of dustry ad busess, the formato s to be collected o labour, cost ad qualty of producto, stock ad demad ad supply postos for proper plag of producto levels ad sales campags. 1.1 Complete Eumerato Oe way of obtag the requred formato at regoal ad coutry level s to collect the data for each ad every ut (perso, household, feld, factory, shop etc. as the case may be) belogg to the populato whch s the aggregate of all uts of a gve type uder cosderato ad ths procedure of obtag formato s termed as complete eumerato. The effort, moey ad tme requred for the carryg out complete eumerato to obta the dfferet types of data wll, geerally, be extremely large. However, f the formato s requred for each ad every ut the doma of study, a complete eumerato s clearly ecessary. Examples of such stuatos are preparato of voter lst for electo purposes ad recrutmet of persoel a establshmet etc. But there are may stuatos, where oly summary fgures are requred for the doma of study as a whole or for group of uts. 1.2 eed for Samplg A effectve alteratve to a complete eumerato ca be sample survey where oly some of the uts selected a sutable maer from the populato are surveyed ad a ferece s draw about the populato o the bass of observatos made o the selected uts. It ca be easly see that compared to sample survey, a complete eumerato s tme-cosumg, expesve, has less scope the sese of restrcted subject coverage ad s subject to greater coverage, observatoal ad tabulato errors. I certa vestgatos, t may be essetal to use specalzed equpmet or hghly traed feld staff for data collecto makg t almost mpossble to carry out such vestgatos. It s of terest to ote that f a sample survey s carred out accordg to certa specfed statstcal prcples, t s possble ot oly to estmate the value of the characterstc for the populato as a whole o the bass of the sample data, but also to get a vald estmate of the samplg error of the estmate. There are

2 varous steps volved the plag ad executo of the sample survey. Oe of the prcpal steps a sample survey relate to methods of data collecto. 1.3 Methods of Data Collecto The dfferet methods of data collecto are: 1) Physcal observato or measuremet 2) Persoal tervew 3) Mal equry 4) Telephoc equry 5) Web-based equry 6) Method of Regstrato 7) Trascrpto from records The frst sx methods relate to collecto of prmary data from the uts/ respodets drectly, whle the last oe relates to the extracto of secodary data, collected earler geerally by oe or more of the frst sx methods. These methods have ther respectve merts ad therefore suffcet thought should be gve selecto of a approprate method(s) of data collecto ay survey. The choce of the method of data collecto should be arrved at after careful cosderato of accuracy, practcablty ad cost from amog the alteratve methods. Physcal observatos or measuremet Data collecto by physcal observato or measuremet cossts physcally examg the uts/respodets ad recordg data as a result of persoal judgmet or usg a measurg strumet by the vestgator. For stace, a crop cuttg expermet for estmatg the yeld of a crop, the plot s demarcated, the crop the selected plot s harvested ad the produce s weghted to estmate the produce per ut area. Data obtaed by ths method are lkely to be more accurate but may ofte prove expesve. Persoal Itervew The method of persoal tervew cossts cotactg the respodets ad collectg statstcal data by questog. I ths case, the vestgator ca clearly expla to the respodets the objectves of the survey ad the exact ature of the data requremets ad persuade them to gve the requred formato, thus reducg the possblty of o-respose arsg from ocooperato, dfferece etc. Further, ths method s most sutable for collectg data o coceptually dffcult tems from respodets. However, ths method depeds heavly o the avalablty of well traed tervewer. Mal Equry I a mal equry, data are collected by obtag questoares flled by the respodets, the questoares beg set ad collected back through a agecy such as the postal departmet. Ths method s lkely to cost much less as compared to above methods. However, the respose may ot always be satsfactory depedg upo the cooperato of the respodets, the type of questoare ad the desg of the questoare. I developg coutres where a large proporto of the populato s llterate, the method of maled questoare may ot eve be feasble. I.17

3 Telephoc equry I telephoc equry, data are collected by questog the respodets. Ths method provdes a opportuty of two-way commucato ad thus ca reduce the possblty of tem orespose. However, ths method ca be used oly for those surveys whch all uts of target populatos have telephoe otherwse t wll cause bas the results. Web-based equry The creasg popularty ad wde avalablty of World Wde Web techologes provde a ew mode of data collecto. I web-based equry, data are collected by obtag questoares flled by the respodets, the questoares beg posted o the et. Oe mportat advatage of usg computer techology data collecto s to mmze the loss of data owg to complete or correctly completed data sets by usg Clet sde valdato. I a era of formato superhghway, ths method s oe of the fastest meas of data collecto. However, developg coutres where a large proporto of the populato does ot have access to Iteret, the method of web-based equry may ot serve the purpose for most of the surveys. Varous Iteret stes are usg ths method for opo poll o certa ssues. Method of Regstrato I the regstrato method, the respodets are requred to regster the requred formato at specfed place. The vtal statstcs regstrato system followed may coutres provdes a llustrato of the regstrato method. The ma dffculty wth ths method, as the case of the mal equry, s the possblty of o-respose due to dfferece, reluctace, etc. o the part of formats to vst the place of regstrato ad supply the requred data. Trascrpto from records The method of trascrpto from records s used whe the data eeded for a specfc purpose are already avalable regsters mataed oe or more places, makg t o more ecessary to collect them drectly from the orgal uts at much cost ad effort. The method cossts complg the requred formato from the regsters for the cocered uts. Ths method s extesvely used sce a good deal of govermet ad busess statstcs are collected as byproduct of route admstratve operatos. 1.4 Varous Cocepts ad Deftos Elemet: A elemet s a ut about whch we requre formato. For example, a feld growg a partcular crop s a elemet for collectg formato o the yeld of a crop. Populato: It s the totalty of elemets uder cosderato o whch ferece s requred. Thus, all felds growg a partcular crop a rego costtute a populato. Populatos may be fte or fte. A fte populato cotas coutable umber of elemets. For example, felds growg a partcular crop a rego are a example of fte populato. O the other had plats of a partcular crop belogg to a large coutry lke Ida s a example of fte populato. Geerally, sample surveys deal wth fte populatos. Samplg uts: A group of elemets costtute a samplg ut. Elemets belogg to dfferet samplg uts are o-overlappg. A samplg ut may have oe, more tha oe or sometmes eve o elemets. Samplg uts are coveet as well as relatvely expesve to observe. For example, t s coveet to select households for collectg data o mlk produced by amals rather tha cotactg the elemets drectly. Samplg uts should be o-overlappg ad physcally detfable. I.18

4 Samplg frame: A exhaustve lst of all the samplg uts costtutes a samplg frame. A example of a samplg frame may be cultvator felds growg a partcular crop or households cotag amals a rego. Sample: A part of the populato selected from a samplg frame for the purpose of makg ferece about the populato s called as a sample. For example, a subset of the cultvator felds may be selected to estmate the yeld of a crop a rego. Sometmes complete eumerato or cesus s mpractcable, mpossble, to collect data o each ad every ut of a large populato. The moey, mapower ad tme requred observg all the populato uts may be cosderably hgh. Moreover, the chace of commttg mstakes creases whe the volume of work s creased. Thus, a sample survey (oly some of the uts of the populato are selected a sutable maer) may be a better alteratve for makg fereces about large populatos. Probablty Samplg: Probablty samplg s a procedure where the uts the sample are selected by a probablty mechasm. Thus, each ut the populato s assged a predetermed probablty of beg selected the sample. The procedure assgs every possble sample a kow probablty of selecto. It s possble to get the frequecy dstrbuto of samples accordg to values of the estmator based o the selected sample. Further, t s possble to determe what proporto of values of estmators wll le a gve terval aroud the true value. o-probablty Samplg: o-probablty Samplg s the samplg procedure whch the uts are selected accordg to the choce of sampler. Thus, the choce of selecto of samplg uts etrely depeds upo the judgemet of the sampler. Frst he observes ad spects the samplg uts ad selects a sutable sample whch he cosders the most lkely to the populato or represetatve of the populato. Ths samplg procedure s oly used for opo surveys ad ot for geeral survey because t s a based method of samplg ad t s ot possble to obta the precso of the estmate from the sample values. Samplg Error: The error whch arses due to use of sample to estmate the populato parameters s called as samplg error. Whatever method of samplg s used, there wll always be a dfferece betwee populato value ad ts correspodg estmate. Ths error s uavodable every samplg scheme. A sample wth the smallest samplg error wll always be cosdered as a good represetatve of the populato. Ths error ca be reduced by creasg the sze of the sample. Thus, whe the sample survey becomes a cesus or complete eumerato, the samplg error becomes zero. o-samplg Error: Besdes samplg error, the sample estmate may be subject to other error whch arses due to falure to measure some of the uts the selected sample, observatoal errors or errors troduced edtg, codg ad tabulatg the results. Geerally, cesus results may suffer from o-samplg error although these may be free from samplg error. The o samplg error s lkely to crease wth crease sample sze, whle samplg error decreases wth crease sample sze. Populato parameters: Suppose a fte populato cossts of the uts U 1,U 2,...,U ad let Y be the value of varable y, the characterstc uder study, for the th ut U, (=1,2,...,). For stace, the ut may be a farm ad the characterstc uder study may be the area uder a partcular crop. Ay fucto of the values of all the populato uts (or of all the observatos costtutg a populato) s kow as a populato parameter or smply a parameter. Some of the I.19

5 mportat parameters usually requred to be estmated surveys are populato total ad populato mea Y Y /. Statstc, Estmator ad Estmate: Y Y Suppose a sample of uts s selected from a populato of uts accordg to some probablty scheme ad let the sample observatos be deoted by y 1, y 2,..., y. Ay fucto of these values whch s free from ukow populato parameters s called a statstc. A estmator s a statstc obtaed by a specfed procedure for estmatg a populato parameter. The estmator s a radom varable ad ts value dffers from sample to sample ad the samples are selected wth specfed probabltes. The partcular value, whch the estmator takes for a gve sample, s kow as a estmate. 2. Smple Radom Samplg Smple radom samplg (SRS) ca be regarded as the basc form of probablty samplg applcable to stuatos where there s o prevous formato avalable o the populato structure. Smple radom samplg s a method of selectg uts out of the such that every oe of the dstct samples has a equal chace of beg draw. I practce a smple radom sample s draw ut by ut. The uts the populato are umbered from 1 to. A seres of radom umbers betwee 1 ad s the draw, ether by meas of a table of radom umbers or by meas of a computer program that produces such a table. At ay draw the process used must gve a equal chace of selecto to ay umber the populato ot already draw. The uts that bear these umbers costtute the sample. Sce a umber that has bee draw s removed from the populato for all subsequet draws, ths method s also called radom samplg wthout replacemet. I case of a radom samplg wth replacemet, at ay draw all members of the populato are gve a equal chace of beg draw, o matter how ofte they have already bee draw. The wth-replacemet assumpto smplfes the estmato uder complex samplg desgs ad s ofte adopted, although practce samplg s usually carred out uder a wthout replacemet type scheme. Obvously, the dfferece betwee wth replacemet ad wthout replacemet samplg becomes less mportat whe the populato sze s large ad the sample sze s otceably smaller tha t. Smple radom samplg serves as a basele for comparg the relatve effcecy of other samplg methods. Estmato of Populato Total Let Y be the character of terest ad Y 1,Y 2,,Y,,Y be the values of the character o uts of the populato. Further, let y 1, y 2,, y,, y be the sample of sze selected by smple radom samplg wthout replacemet. For the total Ŷ y / y.e., the sample mea y multpled by the populato sze. Y Y we have a estmator I.20

6 The estmator ca be expressed as, where Ŷ w y / y w /. The costat / s the samplg weght ad s the verse of the samplg fracto /. Alteratvely, a estmator for the populato total ca be wrtte by frst defg the cluso probablty of a populato elemet. Uder SRS, the cluso probablty of a populato elemet s = /, same or costat for every populato elemet. Based o the cluso probabltes, a estmator of the total ca be expressed as a more geeral Horvtz-Thompsotype estmator 1 Ŷ w y y y. HT I ths case, the estmator Ŷ ad Ŷ HT obvously cocde, because the cluso probabltes = / are equal for each. The Horvtz-Thompso-type estmator s ofte used for example, wth probablty-proportoal to sze samplg where cluso probabltes vary. The estmator has the statstcal property of ubasedess relato to the samplg desg. Varace of the estmator Ŷ of the populato total s gve by 2 ˆ 2 V SRS ( Y ) 1- (Y Y) ( 1) 1 where mea square. Y Y / s the populato mea ad I S (Y Y) /( 1) s the populato A ubased estmator of varace of the estmator Ŷ of the total, V SRS ( Ŷ ) s gve by ˆ ˆ 2 2 V SRS( Y ) 1- (y y ) / ( 1) s / where y square S 2. y / s the sample mea ad s 2 s a ubased estmator of the populato mea 3. Stratfed Samplg The basc dea stratfed radom samplg s to dvde a heterogeeous populato to subpopulatos, usually kow as strata, each of whch s terally homogeeous whch case a precse estmate of ay stratum mea ca be obtaed based o a small sample from that stratum ad by combg such estmates, a precse estmate for the whole populato ca be obtaed. Stratfed samplg provdes a better cross secto of the populato tha the procedure of smple radom samplg. It may also smplfy the orgazato of the feld work. Geographcal proxmty s sometmes take as the bass of stratfcato. The assumpto here s that geographcally cotguous areas are ofte more alke tha areas that are far apart. Admstratve coveece may also dctate the bass o whch the stratfcato s made. For example, the staff already avalable each rage of a forest dvso may have to supervse the survey the area uder ther jursdcto. Thus, compact geographcal regos may form the strata. If the

7 characterstc uder study s kow to be correlated wth a supplemetary varable for whch actual data or at least good estmates are avalable for the uts the populato, the stratfcato may be doe usg the formato o the supplemetary varable. For stace, the volume estmates obtaed at a prevous vetory of the forest area may be used for stratfcato of the populato. I stratfed samplg, the varace of the estmator cossts of oly the wth strata varato. Thus the larger the umber of strata to whch a populato s dvded, the hgher, geeral, the precso, sce t s lkely that, ths case, the uts wth a stratum wll be more homogeeous. For estmatg the varace wth stratum, there should be a mmum of 2 uts each stratum. The larger the umber of strata the hgher wll, geeral, be the cost of eumerato. So, depedg o admstratve coveece, cost of the survey ad varablty of the characterstc uder study the area, a decso o the umber of strata wll have to be arrved at. 3.1 Allocato ad Selecto of the Sample wth Strata Assume that the populato s dvded to k strata of 1, 2,, k uts respectvely, ad that a sample of uts s to be draw from the populato. The problem of allocato cocers the choce of the sample szes the respectve strata,.e., how may uts should be take from each stratum such that the total sample s. Other thgs beg equal, a larger sample may be take from a stratum wth a larger varace so that the varace of the estmates of strata meas gets reduced. The applcato of the above prcple requres advace estmates of the varato wth each stratum. These may be avalable from a prevous survey or may be based o plot surveys of a restrcted ature. Thus, f ths formato s avalable, the samplg fracto each stratum may be take proportoal to the stadard devato of each stratum. I case the cost per ut of coductg the survey each stratum s kow ad s varyg from stratum to stratum a effcet method of allocato for mmum cost wll be to take large samples from the stratum where samplg s cheaper ad varablty s hgher. To apply ths procedure oe eeds formato o varablty ad cost of observato per ut the dfferet strata. Where formato regardg the relatve varaces wth strata ad cost of operatos are ot avalable, the allocato the dfferet strata may be made proporto to the umber of uts them or the total area of each stratum. Ths method s usually kow as proportoal allocato. For the selecto of uts wth strata, I geeral, ay method whch s based o a probablty selecto of uts ca be adopted. But the selecto should be depedet each stratum. If depedet radom samples are take from each stratum, the samplg procedure wll be kow as stratfed radom samplg. Stratfcato, f properly doe, wll usually gve lower varace for the estmated populato total or mea tha a smple radom sample of the same sze. 4. Cluster Samplg A samplg procedure presupposes dvso of the populato to a fte umber of dstct ad detfable uts called the samplg uts. The smallest uts to whch the populato ca be dvded are called the elemets of the populato, ad group of elemets the clusters. A cluster may be a class of studets or cultvators felds a vllage. Whe the samplg ut s a cluster, the procedure of samplg s called cluster samplg. For may types of populato a lst of elemets s ot avalable ad the use of a elemet as the samplg ut s, therefore, ot feasble. The method of cluster or area samplg s avalable I.22

8 such cases. Thus, a cty a lst of all the houses may be avalable, but that of persos s rarely so. Aga, lst of farms are ot avalable, but those of vllages or eumerato dstrcts prepared for the cesus are. Cluster samplg s, therefore, wdely practced sample surveys. For a gve umber of samplg uts cluster samplg s more coveet ad less costly tha smple radom samplg due to the savg tme joureys, detfcato ad cotacts etc., but cluster samplg s geerally less effcet tha smple radom samplg due to the tedecy of the uts a cluster to be smlar. I most practcal stuatos, the loss effcecy may be balaced by the reducto the cost ad the effcecy per ut cost may be more cluster samplg as compares to smple radom samplg. Clearly the sze of the cluster wll fluece effcecy of samplg. I geeral, the smaller the cluster, the more accurate wll usually be the estmate of the populato characterstc for a gve umber of elemets the sample. Thus, a sample of farms depedetly ad radomly selected s lkely to be scattered over etre area, ad thereby provdes a better cross-secto of the populato tha a equvalet sample, e.g. a sample of the same umber of farms, clustered together a few vllages. O the other had, t wll cost more to survey a wdely scattered sample of farms tha to survey a equvalet sample of clusters of farms, sce the addtoal cost of surveyg a eghborg farm s small as compared to the cost of locatg a secod depedet farm ad surveyg t. The optmum segmet or cluster s oe whch would estmate the characterstc uder study wth smallest stadard error for a gve proporto of the populato sampled, or more geerally, for a gve cost. 5. Multstage Samplg Cluster samplg s a samplg procedure whch clusters are cosdered as samplg uts ad all the elemets of the selected clusters are eumerated. Oe of the ma cosderatos of adoptg cluster samplg s the reducto of travel cost because of the earess of elemets the clusters. However, ths method restrcts the spread of the sample over populato whch results geerally creasg the varace of the estmator. I order to crease the effcecy of the estmator wth the gve cost t s atural to thk of further samplg the clusters ad selectg more umber of clusters so as to crease the spread of the sample over populato. Ths type of samplg whch cossts of frst selectg clusters ad the selectg a specfed umber of elemets from each selected cluster s kow as sub-samplg or two stage samplg, sce the uts are selected two stages. I such samplg desgs, clusters are geerally termed as frst stage uts (fsu s) or prmary stage uts (psu s) ad the elemets wth clusters or ultmate observatoal uts are termed as secod stage uts (ssu s) or ultmate stage uts (usu s). It may be oted that ths procedure ca be easly geeralzed to gve rse to multstage samplg, where the samplg uts at each stage are clusters of uts of the ext stage ad the ultmate observatoal uts are selected stages, samplg at each stage beg doe from each of the samplg uts or clusters selected the prevous stage. Ths procedure, beg a compromse betwee u-stage or drect samplg of uts ad cluster samplg, ca be expected to be () more effcet tha u-stage samplg ad less effcet tha cluster samplg from cosderatos of operatoal coveece ad cost, ad () less effcet tha u-stage samplg ad more effcet tha cluster samplg from the vew pot of samplg varablty, whe the sample sze terms of umber of ultmate uts s fxed. It may be metoed that multstage samplg may be the oly feasble procedure a umber of practcal stuatos, where a satsfactory samplg frame of ultmate observatoal uts s ot readly avalable ad the cost of obtag such a frame s prohbtve or where the cost of locatg ad physcally detfyg the usu s s cosderable. For stace, for coductg a soco-ecoomc survey a rego, where geerally household s take as the usu, a complete ad up-to-date lst of all the households the rego may ot be avalable, whereas a lst of I.23

9 vllages ad urba blocks whch are group of households may be readly avalable. I such a case, a sample of vllages or urba blocks may be selected frst ad the a sample of households may be draw from each selected vllage ad urba block after makg a complete lst of households. It may happe that eve a lst of vllages s ot avalable, but oly a lst of all tehsls (group of vllages) s avalable. I ths case a sample of households may be selected three stages by selectg frst a sample of tehsls, the a sample of vllages from each selected tehsl after makg a lst of all the vllages the tehsl ad fally a sample of households from each selected vllage after lstg all the households t. Sce the selecto s doe three stages, ths procedure s termed as three stage samplg. Here, tehsls are take as frst stage uts (fsu s), vllages as secod stage uts (ssu s) ad households as thrd or ultmate stage uts (tsu s). 6. Systematc Samplg I all other samplg methods, the successve uts (whether elemets or clusters) are selected wth the help of radom umbers. But a method of samplg whch oly the frst ut s selected wth the help of radom umber whle the rest of the uts are selected accordg to a pre-determed patter, s kow as systematc samplg. The systematc samplg has bee foud very useful forest surveys for estmatg the volume of tmber, fsheres surveys for estmatg the total catch of fsh, mlk yeld surveys for estmatg the lactato yeld etc. 7. Successve Samplg May tmes surveys ofte gets repeated o may occasos (over years or seasos) for estmatg same characterstcs at dfferet pots of tme. The formato collected o prevous occaso ca be used to study the chage or the total value over occaso for the character ad also addto to study the average value for the most recet occaso. For example mlk yeld survey oe may be terested estmatg the 1. Average mlk yeld for the curret seaso, 2. The chage mlk yeld for two dfferet seasos ad 3. Total mlk producto for the year. The successve method of samplg cossts of selectg sample uts o dfferet occasos such that some uts are commo wth samples selected o prevous occasos. If samplg o successve occasos s doe accordg to a specfc rule, wth partal replacemet of samplg uts, t s kow as successve samplg. Geerally, the ma objectve of successve surveys s to estmate the chage wth a vew to study the effects of the forces actg upo the populato. For ths, t s better to reta the same sample from occaso to occaso. For populatos where the basc objectve s to study the total, t s better to select a fresh sample for every occaso. If the objectve s to estmate the average value for the most recet occaso, the reteto of a part of the sample over occasos provdes effcet estmates as compared to other alteratves. 8. Multphase samplg Multphase samplg plays a vtal role forest surveys wth ts applcato extedg over cotuous forest vetory to estmato of growg stock through remote sesg. The essetal dea multphase samplg s that of coductg separate samplg vestgatos a sequece of phases startg wth a large umber of samplg uts the frst phase ad takg oly a subset of the samplg uts each successve phase for measuremet so as to estmate the parameter of terest wth added precso at relatvely lower cost utlzg the relato betwee I.24

10 characters measured at dfferet phases. I order to keep thgs smple, further dscusso ths secto s restrcted to oly two phase samplg. A samplg techque whch volves samplg just two phases (occasos) s kow as two phase samplg. Ths techque s also referred to as double samplg. Double samplg s partcularly useful stuatos whch the eumerato of the character uder study (ma character) volves much cost or labour whereas a auxlary character correlated wth the ma character ca be easly observed. Thus t ca be coveet ad ecoomcal to take a large sample for the auxlary varable the frst phase leadg to precse estmates of the populato total or mea of the auxlary varable. I the secod phase, a small sample, usually a subsample, s take where both the ma character ad the auxlary character may be observed ad usg the frst phase samplg as supplemetary formato ad utlzg the rato or regresso estmates, precse estmates for the ma character ca be obtaed. It may be also possble to crease the precso of the fal estmates by cludg stead of oe, a umber of correlated auxlary varables. For example, estmatg the volume of a stad, we may use dameter or grth of trees ad heght as auxlary varables. I estmatg the yeld of ta materals from bark of trees certa physcal measuremets lke the grth, heght, umber of shoots, etc., ca be take as auxlary varables. 9. Use of Auxlary Iformato I samplg theory f the auxlary formato, related to the character uder study, s avalable o all the populato uts, the t may be advatageous to make use of ths addtoal formato survey samplg. Oe way of usg ths addtoal formato s the sample selecto wth uequal probabltes of selecto of uts. The kowledge of auxlary formato may also be exploted at the estmato stage. The estmator ca be developed such a way that t makes use of ths addtoal formato. Rato estmator, dfferece estmator, regresso estmator, geeralzed dfferece estmators are the examples of such estmators. Obvously, t s assumed that the auxlary formato s avalable o all the samplg uts. I case the auxlary formato s ot avalable the t ca be obtaed easly wthout much burde o the cost. Aother way the auxlary formato ca be used s at the stage of plag of survey. A example of ths s the stratfcato of the populato uts by makg use of the auxlary formato. 10. Samplg wth Varyg Probablty Uder certa crcumstaces, selecto of uts wth uequal probabltes provdes more effcet estmators tha equal probablty samplg, ad ths type of samplg s kow as uequal or varyg probablty samplg. I the most commoly used varyg probablty samplg scheme, the uts are selected wth probablty proportoal to a gve measure of sze (pps) where the sze measure s the value of a auxlary varable x related to the characterstc y uder study ad ths samplg scheme s termed as probablty proportoal to sze samplg. For stace, estmatg crop characterstcs the geographcal area or cultvated area for a prevous perod, f avalable, may be cosdered as a measure of sze, or a dustral survey, the umber of workers may be take as the sze of a dustral establshmet. Sce a large ut, that s, a ut wth a large value for the study varable y, cotrbutes more to the populato total tha smaller uts, t s atural to expect that a scheme of selecto whch gves more chace of cluso a sample to larger uts tha to smaller uts would provde estmators more effcet tha equal probablty samplg. Such a scheme s provded by pps samplg, sze beg the value of a auxlary varable x drectly related to y. I pps samplg, the uts may be selected wth or wthout replacemet. I.25

11 Refereces 1. Cochro, W.G. (1977). Samplg techques. Wley Easter Ltd. 2. Des Raj, (1968). Samplg theory. Tata-Mcgraw-Hll Publshg Compay Ltd. 3. Hase, M.H. ad Hurwtz, W.H. (1943). O the theory of samplg from fte populatos. A. Math. Statst., 14, Hase, M.H., Hurwtz, W.H. ad Madow, W.G. (1993). Sample survey methods ad theory. Vol. 1 ad Vol. 2, Joh Wley & Sos, Ic. 5. Murthy, M.. (1977). Samplg theory ad methods. Statstcal Publshg Socety. 6. Sukhatme, P.V., Sukhatme, B.V., Sukhatme, S. ad Ashok, C. (1984). Samplg theory of surveys wth applcatos. Ida Socety of Agrcultural Statstcs. I.26