# [R] Two Phase Sampling

From: Mark Hempelmann <e.rehak_at_t-online.de>
Date: Tue 11 Jul 2006 - 23:40:53 EST

Dear WizaRds,

I tried to construct a two-phase sampling design in Survey just the way I hoped understood in Vienna - I was wrong. I think I am too stupid to create the correct subset for phase 2. Phase1: Sample 1000 parts with 80 defective. Phase2: Sample 100 parts out of these 1000 with 15 defective. 0:ok, 1:defunct. The table below gives the conditional sampling values.

library(survey)
ss1 <- data.frame(id=1:1000, ph1.x=rep(c(1,0),c(10,990)), subset=rep(c(1,0),c(100,900)), ph2.y=rep(c(1,0,NA),c(15,85,900)), n1=rep(1000,1000), n2=rep(100,1000) )
table(ss1\$ph1.y, ss1\$ph2.x)

> Phase1.x
>Phase2.y 0 1
> 0 85 0
> 1 5 10

p2 <- twophase(id=list(~id,~id), strata=list(NULL,NULL), data=ss1, subset=~subset, fpc=list(~n1,~n2)) svymean (~ph2.y, design=p2s)

> mean SE
>ph2.y 0.15 0

However, taking into consideration the 2nd sample, the estimator should be:

ph1.x.bar (phase1)=80/1000=0.08 and ph2.y.bar (phase2)=15/100=0.15 defect boards, that means y.est=1.5*0.08=0.12 defect boards, since the RATIO ESTIMATOR equals 15/10=1.5 defect parts for the ratio of defect ph2/defect ph1.

What again did I do wrong? I am positive that the estimator is 12 defective parts per 100 average, so how do I correctly construct the twophase design?

ps: I hope this is not sthg. undergraduates master eloquently...

Thank you so much for your help. I invite you to all the BBQ and beer there is in Europe!

Yours always
mark

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