Let’s say you have limited time and resources to conduct any experiment. Which would be the most effective way to determine whether or not your results indicate a true effect? Taking more smaller samples or taking fewer but larger samples?
Everything points to larger samples sizes being better for reducing variance, but nothing I can find compares size vs effort. Obviously assuming independent sampling, etc.
For example, to determine bug community composition in soil… Should one take many small soil samples, or a couple large volumes of soil?
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I believe this depends on the variability within the sample unit vs between sample units.
Let’s say you want to know the average grade students get. Your You could take a sample of the average from schools or from individual students.
Let’s imagine that every student in a school gets the same grade. In that case you can use schools as your sample unit. You won’t get any more information from looking at the individual students within a school, because they’re all the sample.
The more different students are from one another, the more chance there is for sampling error.
So to know what sampling approach is best you need to know the variance within schools (or estimate it, since to know it you’d have to know all the grades already…). You can then use maths to work out what will get you the most accurate results. Don’t ask me how to do those maths.
That example is relatively easy because there’s a basic sample unit that you can’t go smaller than: the individual. With something like a soil sample it’s a bit more complicated and I don’t know how you’d approach it.
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