Emergency Food Security Assessments (EFSAs) Technical Guidance Sheet No. 11 1

Transcription

1 Emergecy Food Securty Assessmets (EFSAs) Techcal gudace sheet. Usg the T-square samplg method to estmate populato sze, demographcs ad other characterstcs emergecy food securty assessmets (EFSAs) Table of Cotet. Why do populato sze ad demographcs chage a crss?.... What are the key steps the T-square method?.... Whe s t approprate to use the T square method? What are the actvtes for the T-square samplg procedure? What are the lmtatos of the T-square samplg procedure?... 8 Aex : Alteratve T method for use areas wth clusterg of households... 0 Aex : Example of data aalyss from a T sample method... 5 Aex : Table for determg t α... 7 Alde Hederso, cosultat, WFP Food Securty Aalyss Servce, December 008. Techcal Gudace Sheet No. Last updated: February 009

2 Techcal Gudace Sheet No. Last updated: February 009 Usg the T-square samplg method to estmate populato sze, demographcs ad other characterstcs emergecy food securty assessmets (EFSAs) Ths Techcal Gudace Sheet (TGS) descrbes the T-square (T) samplg method, ad provdes gudace ad structos o whe ad how to use the method a EFSA. The T s a samplg desg that ca be used stead of other samplg methods a EFSA survey. The advatage of the T method s that t ca estmate the populato sze ad the umbers of people wth certa characterstcs, such as food securty status, lvelhood or age, wthout costructg a samplg frame. Ths TGS complemets other gudace for EFSAs the EFSA Hadbook., partcular Part IV whch deals wth estmatg umbers of people at lvelhood rsk ad projectg umbers of people eed of assstace.. Why do populato sze ad demographcs chage a crss? A shock such as a tsuam, drought or armed coflct may damage roads, crops ad lvestock, homes, markets ad medcal clcs. Ths destructo creates hardshp for the people who lve or work the affected area. As a result, they may leave for areas that are safer ad that offer better opportutes for food, come, shelter ad securty. These movemets ofte chage the populato sze ad demographcs of both the abadoed ad the resettled areas. Accurate ad tmely formato o the umbers ad locatos of people, ad o ther eeds, s a key elemet of a effectve ad approprate humatara respose.. What are the key steps the T-square method? The T method descrbed ths TGS s a modfed verso of a method used ecology to determe the spatal dstrbuto ad desty of trees ad plats large areas. I ths method, the umber of trees s calculated by measurg the dstace from a radom pot to ts closest tree, or earest eghbour. The dstace to the earest eghbour s related to desty ad, whe multpled by the total area, yelds the total umber of trees a area. Ths TGS modfes the ecology method to estmate huma populato sze ad demographcs by measurg the dstace betwee a radom pot ad a occuped house ad coutg the umber of occupats the house. Secto 4 descrbes how to apply the modfed T method. The key steps are: a. selectg a radom pot; b. measurg the dstace from ths pot to the earest occuped house; c. gog to ths house, fdg the occuped house earest to t, ad measurg the dstace betwee the two houses; d. coutg the umber of people lvg the two houses ad calculatg the average; e. estmatg the total area of the survey; f. calculatg the total umber of houses the survey area by dvdg the total area of the survey by the average space occuped by each house ad ts surroudgs; ad g. calculatg the populato sze by multplyg the umber of houses the survey area by the average umber of people a household. Whe a EFSA survey exames specfc characterstcs of households, such as ther food securty stuato or relace o specfc lvelhood actvtes, these results ca be used to determe the umbers of people wth each characterstc by multplyg the total populato sze by the percetage of people wth the characterstc. See revsed EFSA Hadbook, Part IV Secto, Coductg a stuato aalyss, WFP Food Securty Aalyss Servce, 009.

3 Techcal Gudace Sheet No. Last updated: February 009. Whe s t approprate to use the T square method? The followg questos provde a gudele for whe to use the T. If the aswers to all the followg questos are yes, the T samplg method ca be used. If the aswers to questos a to d are yes, but ay aswer to questos e to h s o, the T should be cosdered wth the other samplg methods suggested, to determe whch s most approprate. a) Is a samplg frame uavalable, urelable or outdated, ad would t be dffcult, expesve or laborous to costruct oe? If YES, the T method may be approprate. If NO, cosder usg a radom, systematc, proportoal or cluster sample. b) Is the samplg frame complex? If YES, the T method ca smplfy the sample desg by reducg the umber of stages. Ths may also reduce the desg effect, thereby decreasg the sample sze ecessary to obta the ecessary precso. If NO, cosder usg a radom, proportoal or cluster sample. c) Is the survey takg place durg the recovery stage of a crss? If YES, the T method may be approprate f there s eough tme. It takes oe or two weeks to detfy ad tra surveyors the method before startg the survey. IF NO, other methods requre less tme ad fewer resources, ad would be more approprate the mmedate post-mpact phase of a acute emergecy. These clude the Delph method, aeral surveys, cluster surveys, quadrat surveys ad usg avalable cesus ad survey data to estmate populato sze ad demographcs. WFP has TGS for cluster ad quadrat surveys, ad the Delph method. d) Is the area where the survey wll be coducted larger tha 0 km? If YES, the T method may be approprate. If NO, cosder a radom, proportoal, cluster or quadrat sample. e) Are most of the houses the survey area sgle-storey resdeces? If YES, the T method may be approprate. If NO, cosder a proportoal or cluster sample. f) Are most of the houses radomly dstrbuted? If YES, the T method may be approprate. If NO, a modfed T method (Aex I) may be approprate, but requres more tme ad resources. g) Are detaled maps avalable? If YES, the T method may be approprate. If NO, use a cluster sample desg to select households radomly. See Techcal Gudace Sheets No. 7 Area Method to Estmate Populato Sze ad Demographcs Emergecy Food Securty Assessmets (EFSAs), A. Hederso, WFP Emergecy Needs Assessmet Servce (ow Food Securty Aalyss Servce), September 007; ad No. 0. Usg the Delph Method to Estmate Populato Sze ad Demographcs Emergecy Food Securty Assessmets (EFSAs), A. Hederso, WFP Food Securty Aalyss Servce, Jauary 008.

4 Techcal Gudace Sheet No. Last updated: February 009 The T method ca be used to fd the radom startg pot for each cluster. h) Are global postog system (GPS) uts avalable to survey teams? If YES, the T method may be approprate. If NO, use a cluster sample desg to select households radomly, ad the T method to fd whch houses to survey. 4. What are the actvtes for the T-square samplg procedure? The T method produces three umbers that are used to calculate the populato sze the target area: ) the total sze of the survey area; ) the average lad area occuped by a household; ad ) the average umber of people a household. The T method ca be dvded to pre-feld, feld ad post-feld actvtes. The ma pre-feld actvtes are detfyg the area to survey ad decdg the level of precso, or marg of error, for the estmate. Feld actvtes clude recrutg ad trag the survey teams, coductg the T samplg procedure ad esurg that resposes are accurately recorded. Post-feld actvtes volve aalyzg ad terpretg the data ad reportg the results Pre-feld actvtes Oce t has bee decded to use the T samplg method the ESFA survey, ad admstratve ad logstcs support are avalable, the ext steps are to defe the area to be surveyed, decde o the marg of error for the survey, calculate the umber of households to sample, ad select ad mark radom pots o the map. a. Defg the area to be surveyed Ths s usually the area where the shock has occurred, people are located ad assstace wll be provded. Geographcal Iformato System (GIS) 4 programs are used to detfy the survey area s borders ad calculate ts surface area. If GIS s ot avalable, Google Earth ( or local maps ca be used to estmate the area to be surveyed. A refemet of detfyg the target area s to clude oly the habted areas the survey area. Ths ca be accomplshed by cludg areas aroud ctes ad vllages ad excludg uhabted areas such as rvers, lakes, deserts, raves, moutas, swamps, parks, forests, etc. Ths wll decrease the amout of area the survey wll cover ad the varablty of the estmate. If the uhabted areas caot be detfed, alterate approaches are to: ) Have GIS programs detfy buffers aroud geographcal features assocated wth habtato, such as roads etc., ad posto radom pots these buffered areas. ) Icrease the umber of radom pots to be surveyed to accout for uhabted areas. Local staff ca defe what costtutes a uhabted area, such as whe there s o occuped house wth km of a radom pot (the horzo s about.7 km away for a perso m tall stadg a flat area), or o house wth a 0-mute walk from the radom pot. The survey team records ths area as uhabted ad moves to the ext radom pot. The umber of pots surveyed should be creased to accout for uhabted areas. b. Decdg the marg of error/level of precso for the survey The marg of error/level of precso for the populato estmate obtaed from the survey ca be: 4 Amog other ageces, the Food Securty Aalyss Servce at WFP Headquarters may be able to provde assstace wth ths. 4

5 Techcal Gudace Sheet No. Last updated: February 009 ± 0 to 0 percet for surveys doe te to 5 days after the shock; or ± 0 percet (or less) for surveys doe 5 days after the shock. The marg of error ca be chaged accordg to how the ESFA results are to be used. For stace, f the EFSA results are to be compared wth prevous or future surveys, a marg of error of less tha 0 percet may be more approprate; the smaller the marg of error, however, the more households have to be surveyed. c. Calculatg the umber of households to be sampled The marg of error s used to calculate the umber of households to be surveyed, whch should be less tha 0 percet of the total households the area. The followg table provdes a gude to the umber of houses to sample accordg to the precso of the survey ad usg a smple radom sample desg. The estmated percetage of the characterstc the surveyed populato refers to the populato characterstc that the survey s measurg secure households, chldre uder 5, farmers, etc. If ths percetage s ot kow, 50 percet should be used as the estmate, because ths produces the largest sample sze. Estmated percetage of the characterstc the surveyed populato Marg of error (%) d. Selectg ad markg radom pots o a map of the area to be surveyed If possble, systematc sample selecto should be used to locate radom pots for the survey. Systematc selecto s preferred because t detfes a pot each secto of the survey area, so the surveyed households are spread across the etre survey area. A radom sample may have clusters of houses oe area, ad/or large areas that are ot sampled Feld actvtes T feld actvtes calculate the average area a household occupes ad the average household sze the target area. These umbers, alog wth the total sze of the target area, are used to estmate the populato sze ad, f addtoal detals are collected, demographcs. The followg steps are carred out the feld: a. Recrutg survey teams: Whe possble, recrut people who have experece of coductg surveys ad kow how to admster a questoare ad record resposes. As a mmum, each team should have oe leader ad oe assstat. The team leader avgates to the radom pot, fds the earest eghbour ad house T (see Fgure ), explas the purpose of the survey to the household occupats ad obtas ther approval for coductg the survey. The assstat measures the dstaces from the radom pot to ts earest eghbour, ad from there to the ext earest eghbour. Both admster the questoare to household T. b. Trag surveyors: Team members eed specal trag o coductg the T method. People take tme to grasp the cocept of fdg the earest eghbour ad cosstetly measurg the dstace betwee the houses. Oe day of trag a morg sesso to expla the cocept ad a afteroo sesso to practse the T sample procedure the feld, followed by a dscusso o ay problems ecoutered helps team members to become comfortable wth ad profcet ths step. c. Obtag maps ad equpmet for the survey: Survey teams eed detaled maps showg the survey area, each radom pot ad earby ladmarks so that they ca fd the boudares of the survey area ad avgate to the radom pots. WFP Headquarters, regoal bureaux or coutry offces may be able to provde these 5

6 Techcal Gudace Sheet No. Last updated: February 009 maps. If ot, they ca be dowloaded from Google Earth ( Fgure ). Methods for measurg the dstaces betwee houses are also eeded. These ca be as smple as trag survey teams to measure ther paces ad cout the umber of paces to reach a house, or to use a tape or rope marked metres. Specalzed measurg tools such as a surveyor s wheel or a laser rage fder speed up the measurg process. d. Navgatg to the radom pot (R): There are two ways of reachg the radom pot, depedg o whether or ot GPS strumets are avalable:. Whe GPS strumets are avalable: GIS software marks the radom pots (R o Fgure ) ad ladmarks the survey area (Fgure ), calculates the dstaces ad drectos from each ladmark to each radom pot, ad provdes the lattude ad logtude of each radom pot ad ladmark. The survey team puts these umbers to a GPS strumet ad uses t to avgate to a radom pot. Ths s best doe by gog to a earby ladmark ad usg GPS to avgate to the radom pot. Oce at the radom pot, the survey team coducts the T samplg as llustrated Fgure.. Whe GPS strumets are ot avalable: Teams mark radom pots o locally avalable maps or those draw by GIS or Google Earth, ad detfy the locatos of earby ladmarks (Fgure ). The survey team uses the map to avgate to the radom pot, where t coducts the T samplg as llustrated Fgure. Fgure. Usg the T method to detfy whch houses to survey Source: adapted from Dggle, 98. Each dot Fgure s a house. The survey team uses GPS strumets or maps to avgate to the radom pot, R. Oce at R, the team vsually locates the earest household (S) ad goes to t. At S, the team looks for the ext earest household (T) wth the hemsphere that s perpedcular to the le draw from R to S. The survey team measures the dstaces from R to S ad from S to T, ad tervews the members of household T. The dstace from R to S s x ad the dstace from S to T s z the formulas used to calculate populato sze ad marg of error. e. Takg measuremets usg the T samplg method: Use Fgure ad the followg structos:. Oce at R, the team marks t wth a coloured flag or stake. It the locates the earest house (S) by vsual observato, ad walks to t. Whe two or more households appear to be at smlar dstaces, the team couts the umber of paces t takes to reach each, to detfy whch s the closest. If two or more 6

7 Techcal Gudace Sheet No. Last updated: February 009 houses are equdstat from R, the oe to be surveyed s selected radomly. The team the measures the dstace from R to S.. At S, the team determes whether the house s occuped or vacat. A vacat house s usually oe where o oe has lved for the past three moths, but survey teams ca use a dfferet referece perod based o local evets or codtos. If S s vacat, the team goes back to R ad selects the ext earest house, repeatg these steps utl the earest occuped house s detfed.. A team member stads frot of the occuped house S, faces R ad exteds her/hs arms outwards. The agle betwee the outstretched arms ad the le from R to S forms the T (Fgure ), but oe of the houses sde ths T ca be selected as house T. The team member turs 80º oe of the houses frot of hm/her ca be selected as house T. The team looks for the earest occuped house house T ad measures the dstace from S to T. The survey s admstered to occupats of house T. 4. The radom pot s completed whe the team has: () measured the dstace from pot R to house S; () measured the dstace from house S to house T; ad () tervewed the occupats of house T. 5. The T sample procedure s desged for areas where each buldg s habted by oe household. Other combatos clude several famles sharg a mult-storey buldg, compoud of several huts, or sgle hut. Typcally, a household s defed as a group of people who eat from the same pot ad sleep uder the same roof. The shock may have chaged lvg codtos so that several famles are lvg oe household, but f they all eat ad sleep uder the same roof, they are cosdered to be oe famly. f. Idetfyg household respodets ad obtag demographc ad other formato: As ay survey, the team leader must expla the purpose of the survey to potetal partcpats, provde ay ecessary formato ad ask permsso to admster the questoare. If a partcpat refuses, surveyors should ask how may people lve the household, or obta the formato from a eghbour. 4. Post-feld actvtes At ths stage, the data are aalyzed ad a report produced o the estmated populato sze ad ts marg of error. As metoed earler, the T samplg procedure produces three umbers for calculatg the populato sze the target area: ) the total sze of the survey area; ) the average lad area occuped by a household; ad ) the average umber of people a household. The total surface area surveyed dvded by the average area occuped by a household dcates how may houses are the survey area. Multplyg ths umber by the average umber of people a household gves the populato sze of the survey area. The followg formula s used: total sze of survey area average area of household F average umber of people household populato survey area The average lad area a house occupes cludes the lad t sts o, the lad assocated wth t garde, amal pe, paths/roads, uhabted structures such as latres, storage, amal housg, etc. ad the lad betwee t ad the ext house. As llustrated the followg example, the report should clude at least the estmated average umber of people the survey area, ad the marg of error ad rage of the estmate. Addtoal elemets ca be the umber of houses sampled, how may were vacat, 7

8 Techcal Gudace Sheet No. Last updated: February 009 ad ay problems ecoutered durg the survey that may have affected the results ad populato estmates. The accompayg Excel spreadsheet cotas formulas that automatcally calculate the populato sze ad cofdece terval whe survey team members put the dstaces betwee houses ad the umbers of occupats. Example The T method determed the followg: a. Average lad area occuped by a household: 50 m. b. Average umber of people a household: 7.6. c. Total sze of target area:.5 mllo m. Total populato:,50,000 m X 7.6 people/house (8,. houses x 7.6 people/house) 6,0 people 50 m Fal results: The total umber of people the survey area s estmated at 6,0. Ths estmate has a 0 percet marg of error, ad the true populato wll be betwee 57,000 ad 69, What are the lmtatos of the T-square samplg procedure? a) The earest eghbour to a radom pot o the edge of the target area may be outsde the survey area, ad teams must select oly houses that are wth the area. I ths stuato, the earest eghbour the survey wll ot be the house closest to the radom pot, so the earest eghbour dstace may be overestmated. The survey team should ote that the true earest eghbour s outsde the survey area, ad that t has used the earest house wth that area. b) Surveyors must uderstad the method ad be able to fd pot R ad houses S ad T, measure dstaces accurately ad use the same pot of referece for each house. c) The referece pot used to measure the dstace from oe house to aother may vary whe the shapes ad szes of houses vary. Survey teams should agree what referece pot the house to use for example, the frot door, a specfc corer of the house, or the mdpot of a specfc wall o the house. At the ed of each day, survey teams should dscuss stuatos where they had to make decsos. The dmesos of houses ca be measured ad reported to show the varato house shape. d) The T method s desged to estmate the desty of households, so t s assumed that the households the sample area are ot clustered. If there s clusterg, the alteratve T method descrbed Aex I should be used. e) As for ay survey method appled the feld, before usg the T method, t s mportat to cosder whether securty, log dstaces ad access to survey areas wll hder survey teams ablty to travel to survey stes. If so, alteratve methods should be cosdered. 8

9 Techcal Gudace Sheet No. Last updated: February 009 Fgure. Sample map for avgatg to a radom pot Detal of area surroudg waypot N, Nearby ladmarks of a market ad a school are detfed wth ther dstaces ad drectos to the waypot. Refereces Byth, K. ad Rpley, B.D O Samplg Spatal Patters by Dstace Methods. Bometrcs, 6: Dggle, P. 98. Some Statstcal Aspects of Spatal Dstrbuto Models for Plats ad Trees. Studa Forestala Sueca, l: 6. Greewood, J.D Basc techques. I W.J. Sutherlad, ed. Ecologcal cesus techques: a hadbook, pp. 0. Cambrdge Uversty Press, Cambrdge, UK. Krebs, C.J Ecologcal Methodology. d edto. Chapter 5. Estmatg Abudace:Le Trasects ad Dstace Methods These Techcal Gudace Sheets, the EFSA Hadbook ad other related resources are avalable at: 9

10 Techcal Gudace Sheet No. Last updated: February 009 Aex I. Alteratve T method for use areas wth clusterg of households Ths procedure s based o the Byth ad Rpley procedure for dstace methods large areas wth clusterg of households; t cludes a step that adjusts for the atural clusterg of households (Byth ad Rpley, 980). The steps the procedure are:. Double the umber of households to survey because two surveys wll be carred out ad two estmates made: oe usg the dstace from a radom pot to a house; the other usg the dstace from a radom house to ts earest eghbour.. Radomly select half of the startg pots. Ths umber s. For example, Fgure 4, the sample s based o three pots; doublg ths meas that sx pots wll be selected. I ths case, radomly select three of the sx pots (marked as uboxed Ps Fgure 4). A survey team goes to each of these three pots ad measures the dstace from t to ts earest occuped household. Ths s the x value. The survey team admsters the questoare to the occupats of the earest household. The followg formula s used to calculate household desty the survey area: ^ N ( x F π Σ ) ˆN estmated populato desty of households the survey area; umber of pots sampled; x dstace from a radom pot to the earest household the survey area.. Aroud each of the remag three pots, mark a small plot cotag about fve households (show as boxed Ps Fgure 4). Number all the households the box ad radomly select households from across all the plots. s the umber of plots ths example, three. Because the three houses are radomly selected from all the houses all the plots, a plot may have o, oe, two or eve three selected households t. I Fgure 4, oe plot cotas o selected households, oe has oe household, ad aother has two. The survey team measures the dstace from the radom pot to the radomly selected house. Ths dstace s z. The team admsters the questoare to the occupats of the household. The followg formula s used to calculate household desty the survey area: ˆ N F π Σ( z ) ˆN estmated populato desty of households the plots; umber of pots/plots sampled; z dstace from the radom household to ts earest household the plot. 4. If N ad N are statstcally smlar (use a T-test), the dstrbuto of houses the survey area s radom. The average of N or N ca be used as the populato estmate the survey area. If N ad N are statstcally dfferet, the dstrbuto of the households the survey area s ot radom, ad formula F4 s used to adjust for the clusterg effect: 0

11 Techcal Gudace Sheet No. Last updated: February 009 N ˆ F4 ˆN estmated populato sze whe calculatg ts geometrc average from ˆN. pot-to-households wth the survey zoe ( ) ˆN ad wth the plots ( ) 5. The marg of error for N or N s calculated by: defg varace as, F5 the varace for each N wll be yˆ F6 ŷ ad the marg of error for each N wll be. s ether N or N ad s the sample sze. F7 6. The marg of error for ˆN s calculated by: defg varace as (/ ) F8 the stadard error s: varace(/ ) F9 ˆ N π Σ( ) F0 x F π Σ( ) z N ˆ F ( ) average area a household occupes; ( ) sample sze; x dstace from the radom pot to ts earest eghbour; z dstace from the radom pot to ts earest eghbour the plot.

12 Techcal Gudace Sheet No. Last updated: February 009 Fgure 4. Sample map for usg the T method a target area wth clusterg of households Source: Krebs, 999. radom pot; house; radomly selected house; survey area; boudary strp aroud survey area; plot. The border of the survey area s marked ad a boudary area about 5 m wde s draw roud ths boudary. Ths survey has a sample sze () of : ( x ) 6, so sx radom pots are selected ad marked systematcally the survey area. Three survey pots are radomly selected for the N method (formula F) ad the three remag pots are used for the N method (formula F). For the N method, a survey team avgates to the radom pot ad fds the dstace to ts earest eghbour. For the N method, the team marks a plot cotag up to fve houses aroud each radom pot, umbers each house the plots cosecutvely, ad radomly chooses houses (three ths case because the sample sze s three) from all the plots. Oce the houses have bee selected, the survey team measures the dstace from the radom pot to radomly selected house(s) the plot. A example of the data ad calculatos volved are descrbed the followg:

13 Techcal Gudace Sheet No. Last updated: February 009 Table. House umber x x z z Number of occupats Sum Average ˆN ˆN ˆN Fgures for x ad z were obtaed from Kerbs, 999: Box 5.. Number of occupats was radomly selected to cetre aroud 6. Usg the umbers Table, calculato of the populato s as follows: ^ N 0 πσ( x ) (.4) 0 πσ( ) (.4)(665.84) ( ) z house/m 40 houses/ha; house/m 96 houses/ha; N ˆ (0.0040)( ) house/m 6 houses/ha. As 40 96, the houses are clustered the survey area, ad N s a less based estmate of the populato. ˆ (/ N) (/ ) (6.5) Varace

14 Techcal Gudace Sheet No. Last updated: February 009 Stadard error varace(/ ) ˆ 0 N Upper 95% CI + tα [ S. E.(/ N)] (.09)(8.075) m /house N house/m 56 houses/ha. Lower 95% CI tα [ S. E.(/ N)] 6.55 (.09)(8.075) m /house N The 95 percet cofdece terval (CI).09 where (see Aex ) house/m 69 houses/ha. t α for - (0-) 9.09 The populato ca be estmated from formula F, usg the survey area ad average umber of people a household (6.9 ths example). The 95 percet CI ca be calculated wth a upper ad a lower 95 percet CI (69 ad 56 ths example). 4

15 Techcal Gudace Sheet No. Last updated: February 009 Example of data aalyss from a T sample method that estmates populato sze ad demographcs Aex. Data from a survey ca be etered the Excel spreadsheet below to obta a populato estmate. Table. Measuremets from a T survey House surveyed Dstace from radom pot R to house S Square of dstace from R to S Dstace from house S to house T Square of dstace from S to T Number of people lvg house T Sum Average x dstace from radom pot R to house S metres (colum ); x square of dstace from R to S (colum ); z dstace from house S to house T metres (colum 4); z square of dstace from S to T (colum 5); N umber of people lvg house T (colum 6); sample sze (0); s x varace of R to S; s covarace of the dstace from R to S ad the dstace from S to T. xz 5

16 Techcal Gudace Sheet No. Last updated: February 009 The desty of houses s estmated as: 0 N T houses/m or.7 Σ [ ] ( 705)[ (797) ] ( x ) Σ( z ) houses/ha. F The stadard error s calculated as: 8( z sx xzxz x sz ) S.E. + + F T 8(797) (40.) + (705)(797)(77.6) + (705) (777.5) Varace of F4 Σx ( x) ( Σx) / 7675 (705) 0 / Σz Varace of ( z) F5 ( Σz) / 465 (797) 0 / ( Σx)( Σz) / 9569 (705)( 797) Σxz / 0 CoVarace of x ad z).9 0 F6 The 95 percet CI for the recprocal of ths desty estmate s: ) F7 ± tα S. E.( ˆ where t α. 7 for 9 (-) degrees of freedom (see Aex T N T 97 ± (.7)(094) or,0 ad 5,845 Takg recprocals gets ad , whch yelds 4.76 ad.7 houses/ha. If the total area s 0,000 ha ad the average umber of people a household s 6., the populato sze s: 0,000 ha x.6 x 6. 05,80 0,000 ha x.7 x 6. 90,8 0,000 ha x 4.76 x 6. 04,6 Thus, the populato sze s 05,00 wth a 95 percet CI of 04,400 ad 0,00. The survey estmated that 6 percet of these people are farmers. To calculate the umber of farmers fd 6 percet of 05,00 4,600. 6

17 Techcal Gudace Sheet No. Last updated: February 009 Table for determg t α Aex. For example, a survey s to have a marg of error of 0 percet. To calculate the cofdece, subtract 0 percet from 00 percet ( percet). The 90 percet ( the cofdece colum o the rght of the table above) s used to fd the t α to be used the Excel spreadsheet to calculate the populato sze. The degree of freedom s calculated by subtractg from the sample sze: where the sample sze. For a sample sze of 0, the degree of freedom s 0 9. The chart does ot have 9, so use the closest degree of freedom, whch s 0. To fd the t α for a sample of 0 at a cofdece of 90 percet, fd the 90% row the frst colum, ad fd 0 o that row. The t α s.7. If the survey has a cofdece of 95 percet ad a sample of 00, the t α s.98. 7