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Appendix A: Multiple-Frame Methods
Pages 163-166

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From page 163... ... with For a the combining supplemental case Suppose that variable y is measured for each MRIP with a supplemental of MRIP survey, with survey, a let supplemental let y y = fish catch survey, i i individual i sampled = fish catch ofofletindividual y individual i = fish in each "i, i,catch ȳ sample survey. For the case"of= s =of individual mean i, ȳfish = fish catch ofmean catch individual combining " fish for i, individuals catchȳ = sample in catch sample meanfor frame fish individuals M who in MRIP with a supplemental survey, let yi = fish catch of individual for individuals in sample frame Mare sample not who in frame are sample M not who in frame are sample notS, ȳin frame" = samplesample S,i, ȳ"frame =mean S, fish sample ȳ" mean =catch sample for me fish n sample frame S,individuals mean ȳfish catch" = forsample in sample individuals catch formean frame individuals fish in individuals catch sample Sin whoin for frame sampleare sample not M who framein frame sample are S S who not who frame in are are M, not sample not inin ȳ % = frame samplesample sample S, frame ȳ frame " mean = M, fish sample M, ȳ % catch = sample mean = samplefor fish individuals mean catch fishforcatc && && ame M, ȳ% = sample mean from sample mean individuals fish fish catch frame catch infor sample Mframe for from individuals in sample theSfrom individuals intersection whoframe are not sample of Mframe insample in theMintersectionframes inframe M, Mof ȳand the intersection % = S, sample sample ȳ of frames "% = mean sample sample Mfish and frames mean S, catch M ȳ fish for and "% = catch sample individuals for me && rames M and S, S, ȳindividuals from "% = =sample sample sample from mean frame mean sample individualsframe fishincatch M fish catch Sfrom for the intersection for in the intersection sample individuals of frame sample from sample Sofframes insample theframeMframes andS inS,M intersection the ȳof and && "% =S, sample p = sample intersection a weighting frames mean of M sample and fish variable S, p catch = a to forweig sample framesframesMbe anddetermined MS,and individuals p = S, afrom plater weighting (see = sample a weighting below) Read the entire page →
From page 164... ... = sample fish catch i, Forfor ȳ" = the caf mean samp uals in sample combining frame MRIPM who with are a not Suppose in supplemental sample that frame survey, variable S, y ȳ let is y = = measured sample fish mean catch for of each fish catch individual i individual fori, ȳ i = sample sampled in mean each fish survey. For combining catch for MRIP individuals with Sin a supplemental sample frame M who survey, " areMletnot yin i = fish sample catch frame of S, individual " = catch ȳfish i, ȳfor sample = "mean sample mean fish mean catch mple individuals inare sample frame who areȳin not in sample frame M, = notsample mean individuals i frame S who catch not in for sample individuals frame M, = sample sample frame mean fish who catch ȳare %for in individuals sample " frame S, ȳ = sample catch for individuals combining in sample MRIP frame with M who a supplementalare not in sample survey, frame S, ȳ = sample mean fish " catch for Mlet ysample i = fish catch ofȳindividual i,mean ȳcatch sample =fish % catchframe individuals forindividuals individuals in insample sample frame &&M in who are not inand =frame S, =mean sample for catc ofMsample frame SMwho aresample ȳSnot sample frame M, ȳframe sample ȳ mean fish fishcatch "for fishindividu && " me Mfrom sample inindividuals the intersection incatch sample in the sample frame inintersection frames S who are frame and not of inS,sample who "% =frame frames are sample not in M,meanȳaresample =not fish sample S,catchȳ%"% mean =M, for sample fish =" sample && %catch for mean individuals catch fo individuals sample frame from Sindividuals sample from in the sample for in frame intersection individuals sample frame Mof inframe S samplethe in in theS sample who intersection are intersection frames M frame andnotof S, in ofM p = who sample sample a %frame frames frames weighting Min M,M variable sample ȳ and and = S,S, to ȳframe sample p = a= S, mean ȳ sample weighting " = fish sample catch mean && LIMITS variable mean for fish fis indivi catch to 164 from sample frame fromMsample frame M inofthe in the intersection sampleintersection frames M RECREATIONAL ofandsample S, ȳ"% FISHERIES && frames% = sample WITH M and "% ANNUAL mean S, fish CATCHȳ"% catch = samplefor mean f Yindividuals in sample frame S who are not infor sample frame M,M ȳ=weighting &&sample be below) Read the entire page →
From page 165... ... and and after after some some SENSITIVITY SENSITIVITY ANALYSIS SENSITIVITY SENSITIVITY ANALYSIS ANALYSIS ANALYSIS manipulation, manipulation, the the ratio ratio can can be be shown shown to to be:be: Increasing the MRIP SENSITIVITY SENSITIVITY survey sample ANALYSIS ANALYSIS size nM increases the value of p, increases the varia Increasing Increasing the the MRIP survey Increasing MRIP the survey MRIPsample sample size nsample survey size M increases sample nsize M increases size nthe nthe valuethe increases of value p,the of p, of increases increases the variance the ratio variance ra @AB(C(DE @AB(C Increasing ) Read the entire page →
From page 166... ... To To provide provide the most benefit in terms of variance reduction, supplemental surveys should be targeted benefit in terms of variance reduction, supplemental surveys should be targeted to MRIP doma to MRIP domains with relatively low MRIP sample sizes (small nM ) and with high variance in y. Read the entire page →

From page 163...

... with For a the combining supplemental case Suppose that variable y is measured for each MRIP with a supplemental of MRIP survey, with survey, a let supplemental let y y = fish catch survey, i i individual i sampled = fish catch ofofletindividual y individual i = fish in each "i, i,catch ȳ sample survey. For the case"of= s =of individual mean i, ȳfish = fish catch ofmean catch individual combining " fish for i, individuals catchȳ = sample in catch sample meanfor frame fish individuals M who in MRIP with a supplemental survey, let yi = fish catch of individual for individuals in sample frame Mare sample not who in frame are sample M not who in frame are sample notS, ȳin frame" = samplesample S,i, ȳ"frame =mean S, fish sample ȳ" mean =catch sample for me fish n sample frame S,individuals mean ȳfish catch" = forsample in sample individuals catch formean frame individuals fish in individuals catch sample Sin whoin for frame sampleare sample not M who framein frame sample are S S who not who frame in are are M, not sample not inin ȳ % = frame samplesample sample S, frame ȳ frame " mean = M, fish sample M, ȳ % catch = sample mean = samplefor fish individuals mean catch fishforcatc && && ame M, ȳ% = sample mean from sample mean individuals fish fish catch frame catch infor sample Mframe for from individuals in sample theSfrom individuals intersection whoframe are not sample of Mframe insample in theMintersectionframes inframe M, Mof ȳand the intersection % = S, sample sample ȳ of frames "% = mean sample sample Mfish and frames mean S, catch M ȳ fish for and "% = catch sample individuals for me && rames M and S, S, ȳindividuals from "% = =sample sample sample from mean frame mean sample individualsframe fishincatch M fish catch Sfrom for the intersection for in the intersection sample individuals of frame sample from sample Sofframes insample theframeMframes andS inS,M intersection the ȳof and && "% =S, sample p = sample intersection a weighting frames mean of M sample and fish variable S, p catch = a to forweig sample framesframesMbe anddetermined MS,and individuals p = S, afrom plater weighting (see = sample a weighting below)

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From page 164...

... = sample fish catch i, Forfor ȳ" = the caf mean samp uals in sample combining frame MRIPM who with are a not Suppose in supplemental sample that frame survey, variable S, y ȳ let is y = = measured sample fish mean catch for of each fish catch individual i individual fori, ȳ i = sample sampled in mean each fish survey. For combining catch for MRIP individuals with Sin a supplemental sample frame M who survey, " areMletnot yin i = fish sample catch frame of S, individual " = catch ȳfish i, ȳfor sample = "mean sample mean fish mean catch mple individuals inare sample frame who areȳin not in sample frame M, = notsample mean individuals i frame S who catch not in for sample individuals frame M, = sample sample frame mean fish who catch ȳare %for in individuals sample " frame S, ȳ = sample catch for individuals combining in sample MRIP frame with M who a supplementalare not in sample survey, frame S, ȳ = sample mean fish " catch for Mlet ysample i = fish catch ofȳindividual i,mean ȳcatch sample =fish % catchframe individuals forindividuals individuals in insample sample frame &&M in who are not inand =frame S, =mean sample for catc ofMsample frame SMwho aresample ȳSnot sample frame M, ȳframe sample ȳ mean fish fishcatch "for fishindividu && " me Mfrom sample inindividuals the intersection incatch sample in the sample frame inintersection frames S who are frame and not of inS,sample who "% =frame frames are sample not in M,meanȳaresample =not fish sample S,catchȳ%"% mean =M, for sample fish =" sample && %catch for mean individuals catch fo individuals sample frame from Sindividuals sample from in the sample for in frame intersection individuals sample frame Mof inframe S samplethe in in theS sample who intersection are intersection frames M frame andnotof S, in ofM p = who sample sample a %frame frames frames weighting Min M,M variable sample ȳ and and = S,S, to ȳframe sample p = a= S, mean ȳ sample weighting " = fish sample catch mean && LIMITS variable mean for fish fis indivi catch to 164 from sample frame fromMsample frame M inofthe in the intersection sampleintersection frames M RECREATIONAL ofandsample S, ȳ"% FISHERIES && frames% = sample WITH M and "% ANNUAL mean S, fish CATCHȳ"% catch = samplefor mean f Yindividuals in sample frame S who are not infor sample frame M,M ȳ=weighting &&sample be below)

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From page 165...

... and and after after some some SENSITIVITY SENSITIVITY ANALYSIS SENSITIVITY SENSITIVITY ANALYSIS ANALYSIS ANALYSIS manipulation, manipulation, the the ratio ratio can can be be shown shown to to be:be: Increasing the MRIP SENSITIVITY SENSITIVITY survey sample ANALYSIS ANALYSIS size nM increases the value of p, increases the varia Increasing Increasing the the MRIP survey Increasing MRIP the survey MRIPsample sample size nsample survey size M increases sample nsize M increases size nthe nthe valuethe increases of value p,the of p, of increases increases the variance the ratio variance ra @AB(C(DE @AB(C Increasing )

Read the entire page →

From page 166...

... To To provide provide the most benefit in terms of variance reduction, supplemental surveys should be targeted benefit in terms of variance reduction, supplemental surveys should be targeted to MRIP doma to MRIP domains with relatively low MRIP sample sizes (small nM ) and with high variance in y.

Read the entire page →

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Appendix A: Multiple-Frame Methods Pages 163-166

Appendix A: Multiple-Frame Methods
Pages 163-166