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Just to add to what the others say, rejecting the null hypothesis is also not evidence that your alternative hypothesis is correct.

Often the hypothesis testing framework is stated something like:

    H0: µ = 0 (null hypothesis)  
    Ha: µ ≠ 0 (alternative hypothesis)
When you reject H0, it means that you can be somewhat confident that there was was some kind of distortion in your data that moved the mean away from (in this case) 0.

You can create a number of theories that purport to explain this mechanistically, but you'll often need particular setups like a randomized controlled trial that can eliminate alternative explanations. When you've eliminated all the competing reasonable hypotheses, there can only be one. If you can use that hypothesis to make non-obvious predictions, that's further proof that it's right as well.

Hypothesis testing is there to tell you when to take an effect seriously, it doesn't tell you whether your explanation is right outside of very carefully constructed circumstances (i.e. where if you see a particular effect, only one theory can explain it).



But the additional theories that you will disprove in further experiments are a subset of Ha so how can disproving H0 not be seen as evidence that Ha is correct. How can H0: the 2 means are equal. and Ha: The 2 means are not equal not encompass the whole universe.

For practical purposes NHST is a function that returns either H0 or Ha.




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