Check out this paper: http://arxiv.org/abs/1311.0081 http://arxiv.org/abs/1311.0081 Your interpretation is fine up until we start using a cutoff and talking ab

Check out this paper: http://arxiv.org/abs/1311.0081 http://arxiv.org/abs/1311.0081 Your interpretation is fine up until we start using a cutoff and talking about significant or not significant results, whether the null hypothesis is true, etc. It is using significance levels that introduces the nonsense.