I understand that we never say that the null hypothesis is accepted, instead we say that the null hypothesis is not rejected since we can never prove an effect does not exist through empirical evidence.
But does the opposite hold? Is there a difference between rejecting the null hypothesis and not accepting the null hypothesis? In the same sense, how can we prove that an effect does exist? Surely we can only show that there is a low probability, say at 1% significance level, that an effect does not exist and thus we can only not accept it?