How to do stratified random sampling in this scenario?

[u/Bubbly_Lobster_9399]

I recently joined a project studying indigenous communities. I unfortunately cannot reveal too many details due to confidentiality. It is related to socio-economic aspects of the communities.

I am studying 3 tribes in 2 geographical regions. The study has both a quantitative as well as a qualitative aspect. The doubt I have is regarding quantitative sampling. I will give a population breakdown

Region 1

Community A = 4558

Community B = 3765

Community C = 2366

Region 2

Community A = 1323

Community B = 676

Community C = 390

How to determine a representative sample which adequately represents all 3 communities? When I used Cochran's (1977) method of estimating sample size, I got a total required sample of 374 (after finite population correction), which then further subdivided proportionally based on the population sizes of each community in each region. However, that made the required sample from region 2 very small (38, 19 and 11 samples for each group in region 2).

My supervisor told me to calculate sample size separately for each community. But doing so gives an unreasonably large sample size which I cannot feasibly cover in the project period.

Need advice. What's the correct method here? Is there any other reputed method other than Cochran's to be used here?

I don't know if this is the correct sub to ask this. I am an economics masters graduate so i thought I'd ask here. I am very new to applied research. I didn't want to rely on AI either

Please help

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[u/wornligament9]

your supervisor’s approach is technically correct if you need each community to stand alone in the analysis, but it ignores the logistical reality you’re dealing with.

the catch is what kind of inferences you’re making. if you’re just comparing regions or looking at the whole population, proportionate stratification is fine even with tiny cells from region 2. those small numbers will have wide confidence intervals but that’s just how it goes with small populations. if you need to do community-level analysis within region 2, you’re stuck between a rock and a hard place because the populations are just too small to avoid a high sampling fraction if you want any precision.

might be worth pushing back on the supervisor with a clear memo showing the numbers both ways and flagging that this is a resource constraint issue more than a pure stats one. sometimes you end up doing a census for the tiny communities and calling it a day