Seeking to understand asymmetry in hypothesis testing

I need to have one understanding on statistical hypothesis testing. In a typical hypothesis test, we have 2 opposite hypotheses; namely Null and Alternative. Here my textbook says that “those 2 hypotheses are not symmetrical in the sense that if we swap the hypotheses then the result will alter”.

Here I am unable to grasp the point which that textbook wants to say. Can somebody explain to me in detail? It would be helpful if someone can give some example of that asymmetry as well.

Appreciate your help.

Thanks,

Answer

I suspect it means that if you perform a test for H1 with null H0 and are not able to reject the null hypothesis, that does not imply that if you performed a test for H0 with H1 as the null that you would be able to reject H1.

The reason is that failing to reject the null hypothesis does not mean that the null hypothesis is true, it could just mean that there isn’t enough data to be confident that the null hypothesis is false.

Attribution
Source : Link , Question Author : Bogaso , Answer Author : Dikran Marsupial

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