Stratified random Sampling. Application for Remote Sensing investigations
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1 Stratified radom Samplig Applicatio for Remote Seig ivetigatio
2 Samplig Populatio: te etire group uder tud a defied b reearc objective Sample: a ubet of te populatio tat ould repreet te etire group Sample uit: te baic level of ivetigatio (e.g., coumer, tore maager, elf-facig, tee, etc. Te reearc objective ould defie te ample uit. Ceu: a accoutig of te complete populatio
3 Reao for Samplig Practical coideratio uc a cot ad populatio ize Iabilit to aalze large quatitie of data potetiall geerated b a ceu Sample ca produce oud reult if proper rule are followed for te draw 3
4 1. Cro-ectioal Tpe of amplig urve a pecific populatio at a give poit i time will ave oe or more of te deig compoet Stratificatio cluterig wit multitage amplig uequal probabilitie of electio. Logitudial urve a pecific populatio repeatedl over a period of time Pael Rotatig ample 4
5 Cro ectioal amplig Mot ued i atural ciece area Baic metod Simple radom amplig Stematic amplig Stratified radom amplig Cluter amplig Double amplig 5
6 Simple Radom Samplig te probabilit of beig elected i equal for all member of te populatio o Blid Draw Metod (e.g. ame placed i a at ad te draw radoml) o Radom umber Metod (all item i te amplig frame give umber, umber te draw uig table or computer program) 6
7 Simple Radom Samplig Advatage: okow ad equal cace of electio oea metod we tere i a electroic databae Diadvatage o Ver iefficiet we applied to kewed populatio ditributio (overad uder-amplig problem) 7
8 Simple Radom Samplig 8
9 Stematic amplig Wa to elect a ample from a director or lit. Ti metod i at time more efficiet ta imple radom amplig. Samplig iterval (SI) populatio lit ize () divided b a pre-determied ample ize () How to draw: 1) Calculate SI ) Radoml elect a umber betwee 1 ad SI a te tartig ample uit 3) Add SI to te poitio umber of ti item ad te ew poitio will be te ecod ampled item 4) Cotiue ti proce util deired ample ize i reaced 9
10 Stematic amplig Advatage: Kow ad equal cace of a of te SI cluter beig elected Efficiec..do ot eed to deigate (aig a umber to) ever populatio member, jut toe earl o te lit (ule tere i a ver large amplig frame). Le expeive fater ta SRS Diadvatage: Small lo i amplig preciio Potetial periodicit problem 10
11 Stematic amplig 11
12 Stratified Samplig Ued we te ditributio of item i kewed. Allow to draw a more repreetative ample. Hece if tere are more of certai tpe of item i te populatio te ample a more of ti tpe ad if tere are fewer of aoter tpe, tere are fewer i te ample. 1
13 Stratified amplig Baic idea: Te populatio i eparated ito omogeeou group/egmet/trata ad a ample i take from eac. Te reult are te combied to get te picture of te total populatio. Sample tratum ize determiatio Proportioal metod (tratum are of total ample i tratum are of total populatio) Diproportioate metod (variace amog trata affect ample ize for eac tratum) 13
14 Stratified amplig Advatage: More accurate overall ample of kewed Relative efficiec (RE) RE SE SE SRS STRS Overall field meauremet are uuall le expeive Diadvatage: More complex amplig pla requirig differet ample ize for eac tratum 14
15 W Stratified Samplig i more accurate for kewed populatio? Te le te variace i a group, te maller te ample ize it take to produce a precie awer. W? If 99% of te populatio (low variace) agreed o te coice of brad A, it would be ea to make a precie etimate tat te populatio preferred brad A eve wit a mall ample ize. But, if 33% coe brad A, ad 3% coe B, ad o o (ig variace) it would be difficult to make a precie etimate of te populatio preferred brad it would take a larger ample ize. 15
16 W Stratified Samplig i more accurate for kewed populatio? Stratified amplig allow te reearcer to allocate a larger ample ize to trata wit more variace ad maller ample ize to trata wit le variace. Tu, for te ame ample ize, more preciio i acieved. Ti i ormall accomplied b diproportioate amplig. 16
17 Stratified amplig 17
18 Pae i tratified amplig Tree pae i completig a tratified amplig cruie: 1. Plaig 1. Plot ize/traect legt ad ape. Sample ize determiatio 3. Cruie laout. Field meauremet Data collectio 3. Data proceig ad Reportig Computatio tad ad tock table Reportig 18
19 Plaig Stratified amplig: ample ize Sample ize ad allocatio Sample ize: imilar to SRS Allocate amplig uit amog trata Equal allocatio: ame # ample uit regardle trata ize Proportioal allocatio: # ample uit proportioal to te relative ize of trata ema allocatio: # ample uit depeded o trata SIZE ad VARIATIO 19
20 Equal: Prop.: Plaig Stratified Samplig: ample ize Allocatio Stratum Wit replacemet Witout replacemet ema : Sample ize ad tratum ize H t H t H SE SE t 1, α/ 1, α/ + 1, α / t t SE 1, α/ 1, α/ SE + t 1, α / t 1, α/ ( ) t 1, α/ ( ) + 1, α / SE SE t Te otatio follow te mbolog of Cocra WG (1977) Samplig Tecique. Wile &So 1977 wic i imilar to te oe ued b Free F (196) Elemetar Foret Samplig. USDA Foret Service. Agriculture Hadbook 3. 0
21 Plaig: ample ize Deer populatio i Louiiaa Area of iteret: 40,000 q mi Plot ize:.0 x q mi Helicopter deer coutig 1
22 Plaig: ample ize Deired amplig error i idividual from true value: SE ote: te SE i for te etire cruie ot for eac trata Stratificatio accordig to vegetatio tpe Ope: 8000 q mi Srub: 16,000 q mi Deciduou & Coiferou: 1,000 q mi Coiferou: 4,000 q mi Stadard deviatio etimated uig remote eig iformatio, or b pre-amplig or from literature: Ope Srub Dec&Coif Coif
23 ample ize Determie te ample ize 40,000 / 4 10,000 1 ope 8,000 / 4,000 rub 16,000 / 4 4,000 3 Dec&Coif 4 Coif 3
24 Plaig: ample ize Firt compute te total ample ize: 1. Select te allocatio procedure. Iterate accordig to. Ti mea tat te computed ould be equal to te from te t ditributio. Equal allocatio Proportioal allocatio ema allocatio / 1, SE t H α / 1, SE t α /, 1 ) ( SE t α 4
25 Plaig: ample ize Secod compute te ize of eac trata uig te elected allocatio: ema allocatio: 5 coif coif decid rub ope &
26 Leged Ope Srub: Decid.&Coif. Coiferou Plaig: cruie laout
27 Field meauremet Te data would be recorded a i SRS Hierarc wit two level: Strata firt level Plot # witi te trata A tird level could appear witi te trata, e.g. product 7
28 data proceig 8 T T T T i i i t t i i i i ± ± / 1; / 1; total for limit Cofidece total te of deviatio Stadard : Total mea for limit Cofidece tadard error) (aka mea te of deviatio Stadard 1 ) ( 1 ) ( Variace : Mea : α α Stratum value etimate
29 Data proceig 9 Overall value etimate T T T EDF T T T T EDF T T t t ± ± / ; / ; total for limit Cofidece total te of deviatio Stadard : Total mea for limit Cofidece tadard error) (aka mea te of deviatio Stadard ) ( Mea : α α EDF T
30 Data proceig Ivetor o 150 ac. Foret tratified i tree differet trata: 1. Lobloll Pie@0 ear old: 500 ac. Mixed ardwood@45 ear: 500 ac 3. Lobloll ear: 50 ac Stratified radom amplig wit plot ize of 0.1 ac Objective:: determie volume/ac, volume/foret tpe & total volume 30
31 Computatio H 3 (umber of trata) Data proceig 150 ac/0.1 ac 1,500 plot / 150 x , / 0.1 5, Samplig trateg: STRS wit ample ize 30 plot equal allocatio ote: witi trata SRS 31
32 Data proceig Te total volume for eac plot wa determied (uig te fixed area plot procedure) ad ummarized i te table bellow: Stratum 1 Stratum Stratum
33 Data proceig Statitic Stratum 1 Stratum Stratum 3 Mea Variace Std. deviatio Std. error mea Std. error STRS Volume [ft 3 /ac] CI for Vol./ac Total Volume [ft 3 ] CI for Total Vol. Mea SRS Std. error SRS Relative efficiec 33
34 Data proceig Statitic Stratum 1 Stratum Stratum 3 Volume [ft 3 /ac] Std. error mea Weigt Volume STRS [ft 3 /ac] Std. error STRS Volume SRS [ft 3 /ac] Std. deviatio SRS Wat i te ample ize for SRS to acieve te ame level of accurac a STRS? SRS t-1; α SE
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