Can you actually prove if the null hypothesis is true or a type II error has occurred?
I'm new to statistics (sorry in advance!)
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4$\begingroup$ Yes…if you knew the answer before you ran the hypothesis test. That sounds ridiculous, but it can be important to simulation studies. $\endgroup$– DaveCommented Jun 13, 2021 at 0:21
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2 Answers
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No, you cannot. The are indistinguishable and this is one of the key challenges in statistics. An alternative comparison can be made between finding a significant result (because H0 is false) vs a type 1 error. We can attempt to control these error rates but it is always a trade off.
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No, but non rejection makes you take a decision. So it acts as if you proved the null in practical sense
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$\begingroup$ I kind of follow what you mean, but this is such confusing phrasing for a newcomer to statistics. $\endgroup$– DaveCommented Jun 13, 2021 at 16:38