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I have multiple characteristics of a population available (gender, age, place), and I have the answer for each individual for a particular yes-no question available done previously. For example, here is a sample population.

pop = data.frame(y=c(1,1,0,1,0,1,0,1,0,0,0), 
                 gender=c(1,1,0,1,0,0,1,1,0,0,0),
                 age=c(21,20,45,32,20,19,33,20,34,35,22),
                 place=c(1,3,2,4,1,3,5,2,1,5,2))

I want to ask the same question to the same population again. The answer may have changed, but there is a reasonable expectation it may not have. What is the way to decide which of these characteristics (single or in combination) is best to use as a strata in stratified sampling to reduce the error? More importantly, how do I justify my choice? (Can I base it on some statistics of the previous)?

I understand from this question answers that running an anova for each strata might help.

> anova(lm(y~place+gender+age, data=pop))
Analysis of Variance Table

Response: y
          Df  Sum Sq Mean Sq F value  Pr(>F)  
place      1 0.00147 0.00147  0.0086 0.92852  
gender     1 1.17581 1.17581  6.9329 0.03376 *
age        1 0.36281 0.36281  2.1392 0.18697  
Residuals  7 1.18719 0.16960                  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

So I should probably use gender alone as the strata here. Others are not of much use. Is this the correct way?

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  • $\begingroup$ I am not sure what you need. I would simply structure the dataset leaving on the same row the first and second reply for each subject, or create a new row for each subject but use an identifier to enable clustering 1:1 by individual. $\endgroup$ – Joe_74 Mar 29 '16 at 8:12
  • $\begingroup$ I didn't understand what you mean. Did you mean I should remove the data frame assignment and format the data as a table? $\endgroup$ – rahul Mar 29 '16 at 16:47

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