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Hmm, I tried playing around with this tool.

When I enter 250000 in sample size I get ranges that don't overlap. Does that mean I would need that many samples to answer this?

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Yes. The bigger your sample size, the bigger your ability to see small effects. A test with 1000 elements can only tell apart big effects; a test with 250000 can tell apart much smaller ones. This is the idea of https://en.wikipedia.org/wiki/Statistical_power

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