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# Applied Sampling for Wildlife FW 580

CSU

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This 7 page Class Notes was uploaded by Maximilian Lynch on Monday September 21, 2015. The Class Notes belongs to FW 580 at Colorado State University taught by Staff in Fall. Since its upload, it has received 33 views. For similar materials see /class/210053/fw-580-colorado-state-university in FISH at Colorado State University.

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Date Created: 09/21/15

FW 580 IWhat were take home messages from last time When should you stratify Effect of uniform sampling Variable effort Cluster sampling ISelect sample size of 2 by randomly picking one cluster quot vs 426 from SRS Cluster sampling IExcel example IWe picked a random cluster of 2 IMean unbiased IPrecision poor 6 vs 4267 from SR5 Cluster Sampling IThe superficial resemblance to stratification is that clustered sample units are grouped like a stratum ISelection process is different In stratification every strata is sampled In cluster sampling select among clusters in same way as SRS 0Then use all units in cluster Cluster sampling Iis SRS applied to groups of population members each group being considered as a single unit in the selection process With or without replacement List or systematic sampling ISay a list of N100 members is the population to be sampled lCan divide list into n sublists where n is the sample size desired and serially number each sublist from 1 to n IA single number r between 1 and Mn is chosen by a SR process and each individual whose number is r is selected for the sample IThis is not stratified or SRS because the selections are dependent upon a common random procedure Cluster sampling principle IAs in stratification the sampling variance of the estimator depends on the way in which we form the clusters IExcel example Cluster sampling effect of different clustering schemes p l Cuunl Scheme 5 Scheme 0 2 l E E in mmoomgt lEI l2 TRUEAve 8 Scheme 3 Scheme 0 Sample Membevl Membea Amage Deviance 2 Membevl Membea Average Deviance 2 l 2 s 4 ha 2 l2 7 l a in a l s in a u 3 in l2 ll 9 a in a l Amage a a Variance a 57 u 57 vs 426 from SRS or 6 for Scheme A Cluster sampling ICS B sampling variance much larger than CS A ICS C sampling variance is extremely small Dependence of cluster sampling variance upon cluster formation is much more marked than the phenomenon in strati ed sampling Sampling variance in Bis 13X that in C hy Cluster sampling ICluster sample B 2 smallest values in a cluster 2 next smallest in a cluster and the 2 largest in a cluster Matches individuals within clusters as much as possn e ICluster sample C mismatches as much as possible Cluster sampling principle IFor maximum precision in cluster sampling clusters should be formed so that the individuals within a cluster vary as much as possible lClusters are as much alike as possible Compare with strati cation Cluster sampling IGains in precision can be made IHowever usually not the case since clusters are often formed by proximity ie individuals are alike contradicting the principle Cluster sampling vs SRS ISay you want to take a sample of 100 field plots Could RS 100 plots Could RS 50 clusters of 2 ILater method has economies in cost but 4 Cluster principle revisited ICluster sampling will be more precise than SRS with the same sample size if the individuals within clusters vary more on the average than do the individuals in the population as a whole The greater variation within clusters the greater precision of cluster sampling Cluster sampling IIn practice we are not likely often to achieve gains in precision by cluster sampling the opportunity to construct good clusters seldom occurs ISometimes worthwhile to incur larger sampling variance if costs can be proportionally reduced lReconciling precision and costs important Variablesized clusters 1 l l 10 l l l l l l 3 l 12 l l l l 12 l 12 l 6 l l l l l l l l Bil l l B l l l l l leiEDI mama l 267 Not an equal Qute good Less than probabllltysdneme halfofsdweme A Variablesized clusters IOften can t fix sample size within a cluster First time we encounter sample size as a random variable Excel example IWhen proper weighting is used unbiased estimation will hold IVariablesized clusters as for equalsized it is the con guration of individuals that matters List systematic sampling revisited lIf clusters have the same variation as the population as a whole the cluster sampling and SRS will give the same answer lList systematic sampling often treated as a SRS Systematic sampling caution lPeople like because of spatial balance later lIf periodicity of the systematic sample is similar to an underlying but unknown periodicity in the population of interest sample is not representative biased 4 Stratification lBasically a precisionincreasing device Divide population into subgroups strata Calculate statistics for each stratum and then combine to give estimates for the population as a whole With a uniform sampling fraction almost always gain Cluster sampling ISuperficial resemblance to stratification Actually sharply contrasts IUsually lose precision lOnly use when offsetting costs compensate Greater precision per unit cost Cluster sampling ITO date everything we have discussed SRS stratification with and without replacement uniform or variable fractions have an element in common Selection process selects one member of the strata or population at one time Sampling units are not associated or tied toget er Sampling schemes Simplerandom sampling SRS all sampling units have the same probability of being selected Stratification lWant variances similar within strata TLarge differences between strata Can almost never go wrong with stratification Systematic I Spatial bala I Po pular and o en treated as SRS I ten a aw variances underestimated Measurements along environmental gradienE Correlated measures among adjacent individuals etter to use multiple ta 39 Spatially Ba lanced Samples Stevens and Olsen 2004 lGeneral Randomized Tessellation Stratified GRTS sample lAdvantages Spatial balance spread outquot Ease with which units can be added to stu Avoids alignment problems as in system 39 ITheory and details difficult to understan partly because of the flexibility as Spatially balanced details I Recursive mappin I Switch from base10 to base2 or base4 numbers 0 n 1 2 3 o o H o 4312 1 1 Free software a 39 both GIS tools and standalone programs SDraw McDonald 2993 FW 580 Double or Twophase FW 580 Double or Twophase sampling sampling An initial sam leis selected to obtain augtltiia ltMn ratio and regreSSIon estimation we I information o ly rY used supplementary information to gain 0A second sample often subsample of first is more preCIse estimates chosen to observe variable of interest in addition to auxiliary I Nleided aUXIIIary varlable for a possmle 0 Purpose is to obtain better estimates by using p o 5 relationship between two varia es Not always available for all plots and we 9 Exampe57 need to sample for the auxiliary variable Waterfowl sune s 9 Increased sampling variance What about nonresponse in call surveys Moose example Nonsampling errors 0240 moose seen in 20 plots aerial QDifferences between estimates and survey 100 plots in sample frame population quantities that do not arise H5 plots had 56 from air and 70 from from the feet that a sample net the foowup ground survey whole population is observed 07056 125 Or detection 7 eExamples Estimate of total moose Sensitive topics drug use poaching Detection issues Nonresponse Random response model Can incorporate stratification into the ONonsampling error second subsample What might you Truthfulness with sensitive questions a Drug use infidelity poaching overestimation Setup Designate people in population as having characteristic A or not B two groups Let p be the proportion of people in group A Objective is to stimate p stratify upon in a calling survey Random response model example OStart with deck of identical cards except some fraction 9 is marked with A and th remaining 1 e is marked with B A sample of people are chosen and each IS asked to randomly draw a card and state yes if they agree with the letter on the card or no othenNise replace card e OThe interviewer doesn t see the card just records yes or no Random Response Poles 910 1 91 P Pyes p297l 17 9 quotye 522971179 n tot 3 my 7 jwhere 5 l 2671 nm 2671 2 Random Response 0 Tree diagram Yes 1170 E 12 H 2 1p no A lt 1 yes E 7 E 1 1 2 Tlt nm 2 4 12 no Random response model example Twostep process 1 select card 2 decide whether or not ou belon to group on card QTree diagram A yes 6 A lp B A 19 P B ln B Yes Many variations 2 questions A have you ever exceed your limit B Is the second to last diit in our phone number odd Respondent flips a coin and answers A if heads B if tails Many variations Use what is most likely to elicit a response Usually need a large sample size

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