# What are the optimizations or goals to consider when using stratified sampling?

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?

• 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. – djhurio Nov 7 '12 at 6:52
• Is this a duplicate account: stats.stackexchange.com/users/11832/jane-wayne? – chl Jan 11 '13 at 21:56

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