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In stratified sampling, what are the optimization considerations? For example, the sample size per stratum could be defined with proportional allocation as $n_h=n\frac{N_h}{N}$, where $N_h$ is the population size for stratum $h$, $N$ is the total population size, $n$ is the total sample size, and $n_h$ is the sample size for stratum $h$.

For a binary variable, I can choose $n$ so that my margin of error $e$ is 1%, 5% or 10%. $$e=z_{1-\frac{\alpha}{2}} \sqrt{\frac{pq}{n}}$$

I could also choose my $n = \sum_{h=1}^H n_h$ such that the margin of error for each stratum $e_h$ is 1%, 5% or 10%. $$e_h=z_{1-\frac{\alpha}{2}} \sqrt{\frac{pq}{n_h}}$$

But my question/concern is, how many different considerations are there and which ones are the most important ones in the context of stratified sampling?

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  • $\begingroup$ Depends what is your goal and what constrains do you have. For example, if you have fixed sample size Neyman Allocation will allow to estimate population total with minimum variance. $\endgroup$ – djhurio Nov 7 '12 at 6:52
  • $\begingroup$ Is this a duplicate account: stats.stackexchange.com/users/11832/jane-wayne? $\endgroup$ – chl Jan 11 '13 at 21:56
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There could be many optimisation goals considered, for example:

  • Minimise the variance for the estimator of population total under fixed sample size
  • Minimise the variance for the estimator of population domain total under fixed sample size
  • Minimise the variance for the estimator of population total under fixed survey cost
  • Minimise the cost of survey under fixed variance for the estimator of population total

Good reference could be Kish, L. (1965). Survey sampling. New-York: John Wiley & Sons

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