In stratified sampling, if each stratum is designed with a fixed margin of error (MOE)—for example, 3% per stratum—does the overall margin of error for the combined sample necessarily decrease when analyzing the entire sample?
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1$\begingroup$ Shall we presume you are referring to the MoE of the grand mean of the population? If not, could you please explain what you mean by "analyzing the entire sample"? $\endgroup$whuber– whuber ♦2025-02-24 13:40:15 +00:00Commented Feb 24 at 13:40
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$\begingroup$ Not necessarily but if you say more about your situation we can help you figure out if it does in this case. $\endgroup$Josh– Josh2025-02-24 14:47:02 +00:00Commented Feb 24 at 14:47
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$\begingroup$ A related inquiry concerns what you mean by "decrease:" with multiple strata there is one MoE for each stratum, so which of those MoEs are you inquiring about? All of them? At least one of them? There's also an issue of how you are computing these MoEs. For instance, the answer could change if you're using a regression estimator instead of an arithmetic mean estimator for a population mean. $\endgroup$whuber– whuber ♦2025-02-24 15:18:28 +00:00Commented Feb 24 at 15:18
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