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I have a population around 300,000 students who are in around 1000 schools. Out of these 1000 schools there are 50 "special schools". All schools fall into 70 districts (which are themselves in 14 zones). How should I think about sampling technique? [Multi-stage cluster or stratified etc.]

This is a case where I would like to take the students' opinion on a teaching tool and how they used it.

What should be the ideal sample size? In this regard I have a basic question: take Yamane's (1967) formula; what is exacty meant by confidence interval of 95%?

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  • $\begingroup$ The most important thing that you didn't mention is what is aim of your study? What do you want to measure? What questions are your asking? E.g. if you are interested in finding if girls are taller than boys in general, than you could possibly ignore most of the hierarchical structure of the data and sample students randomly... $\endgroup$ – Tim Jan 19 '16 at 8:41
  • $\begingroup$ @Tim: Thanks. I would like to know what they think of a teaching tool and how did they use it. $\endgroup$ – Abhimanyu Arora Jan 19 '16 at 8:44
  • $\begingroup$ Please edit to add the details to your question. $\endgroup$ – Tim Jan 19 '16 at 8:47
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Since you already have all the information about zone, region, district, and school, you should probably just do random sampling. Stratify based on school if you think it's important to have each one equally represented. The ideal sample size is as large as you can handle.

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  • $\begingroup$ Thanks. I didn't quite get your point on having information on the levels...it would be really nice if you could make me understand $\endgroup$ – Abhimanyu Arora Jan 19 '16 at 8:46
  • $\begingroup$ As far as level of stratification is concerned, can't it be district? $\endgroup$ – Abhimanyu Arora Jan 19 '16 at 17:06
  • $\begingroup$ This answer is absolutely incorrect. Simple random samples are never drawn in this situation. SRS would require a list of all 300,000 students from which the SRS could be drawn and its cost would be prohibited. Stratifying "by school" is also infeasible, as it would require that every school be visited $\endgroup$ – Steve Samuels Jan 21 '16 at 3:00
  • $\begingroup$ Well, this was answered before the question was edited, when it implied that the data was already collected and just needed to be subsampled. $\endgroup$ – Nuclear Wang Jan 21 '16 at 10:02
  • $\begingroup$ @Nuclear Wang: Then maybe you could edit your answer to make it relevant, or delete it else? $\endgroup$ – kjetil b halvorsen Mar 7 at 20:08

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