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Say I have a test - let's say for some chemical. I have 15 fields, which I divide in half. On the left side of the field, we dump some chemical into the field, on the right side, we do not. We record the bunny population before and three months after. Is it possible to construct a statistical test to say the chemical had NO effect, rather than trying to prove the chemical had an effect? Is this just a chi-square?

Carbon
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    Many questions about this on site already. (e.g. try searches on *prove the null* or say *accept the null*) There's some useful discussion [here](https://stats.stackexchange.com/questions/6225/is-it-possible-to-prove-a-null-hypothesis) among many others. As a practical matter consider interchanging the hypotheses in the test test: a point alternative (previously the null) for a continuous parameter not at a boundary vs a (complementary) composite null has all manner of difficulties, ...ctd – Glen_b Oct 31 '17 at 03:16
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    ctd... from the difficulty of obtaining a null distribution to a lack of power (there will always be a null closer to the data than the alternative is). A practical approach is offered by equivalence /noninferiority testing. Consider that the chemical must almost certainly have at least *some* effect (even water will); the question will be whether the effect is so small that it's negligible. In essence, define your interval of "equivalence" (negligibility) and show that the effect doesn't lay outside that interval. – Glen_b Oct 31 '17 at 03:29
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    For two simple or two composite hypotheses, there's a bit more scope for comparing them by interchanging the hypotheses. – Glen_b Oct 31 '17 at 03:41

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