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I have a total population of 4,000 farmers, divided into three unique regions. Approximately 50% of the farmers live in Region A (N=2,000), 27% in Region B (N=1,080), and 23% in Region C (N=920). I am trying to calculate the needed sample size for a cross-sectional survey with a 10% margin of error and 95% confidence to capture a representative understanding of how much of their corn harvests they are saving for home consumption.

I don't have enough information about where the farmers are living to employ a cluster randomized study design, but I do acknowledge that there will likely be regional differences which is why I'd like to at least stratify my sample by the three regions mentioned above.

Given that the distribution between strata is skewed, what is the best practice in calculating sample size in order to ensure overall representativeness of the "total universe of our farmers (N=4,000)", and then ideally be also able to discuss results at the regional level.

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    $\begingroup$ You need a hypothesized measure of effect and its variability, like a mean and standard deviation. If response rate and effect is homogeneous across strata, the optimal design is still SRS. If you wish to summarize response across strata, or for measures which vary across strata, the optimal design will oversample in the smaller strata. $\endgroup$ – AdamO Mar 14 at 20:27

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