Multi stage sampling for a nationwide study:
We are planning a study comprised of assessing teaching (through classroom observation) and SLO (test) from public and private schools of six provinces of X country.
We need to include all six provinces.
-> there is variation in number of districts in each province. How many districts should we select and on which basis?
-> Should we need to do power calculation for school level? if yes, should we consider entire schools of the province as population and select schools from it? How many schools should be select from each district?
-> From each school we want to have representation from primary (1-5) and lower secondary grades (6-8). How many grades should be select? and on which basis?
-> How many students would be enough from each school? Can we use power calculation for students? if yes, what will be our population?
Also, would be grateful if you could suggest some relevant references and useful sample calculation calculators.
Looking forward to hear from you.
Thank you
This is a complex design and if possible, I suggest you consult a statistician at your home university.
One thing to note is that your "clustered" design will yield non-independent observations, so you should use multi-level modeling in your analyses.
I'm going to address some conceptual issues. First, surveying 6 to 8-year-olds is not common, as reading levels are different. Secondly, most large-scale surveys are piloted in year 1. Thirdly, are you providing school-level data? Anonymity and confidentiality concerns arise. Fourth, psychometric properties, such as Rasch analysis, etc., become important. Fifth, without computer administration, any survey would require great staff intensity.
What you propose has been done, though many organizations, due to costs, only survey every 2, 3, or 5 years, etc. Maybe you should contact an organization that has carried out such a large project, like the University of Chicago and the 5 E.
Maybe you can use cluster sampling. Because that way you can see the comparison of data from the region or sample you are using
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