# “Accept null hypothesis” or “fail to reject the null hypothesis”? [duplicate]

I'm trying to conduct a Student's t-test for a table of values while trying to follow the explanation and details found on this website. I understand that if the p-value is

• <.01 then it's really significant
• >.05 it's not significant
• in between then we need more data

But on that page they seem to accept their null hypothesis no matter what the p-value is. So I'm really not understanding now when to accept or reject the null hypothesis.

• When you do you accept or reject the null-hypothesis?
• Is it true that you are never supposed to accept your null hypothesis, but rather reject or fail to reject the null?

## marked as duplicate by Silverfish, whuber♦Dec 12 '15 at 17:17

• You are right: If the $p$-value is >.05, we often say that we fail to reject the null hypothesis or that we don't have evidence to suggest that the means are different. This does not mean that the null hypothesis is true. But they explain it on the website: "In science, when we accept a hypothesis, this does NOT mean we have decided that the hypothesis is correct or that it is probably correct." I doubt if "accept" is the best term in this case as it can lead to confusion. – COOLSerdash Jun 2 '13 at 16:57
• This article here also advocates that the term "accept" should not be used by scientists. – COOLSerdash Jun 2 '13 at 17:19
• The explanation on that website is very poorly worded. – Peter Flom Jun 2 '13 at 21:08
• "fail to reject the null hypothesis" (or something similar) is the way I generally put it on the rare occasions when I formally test a hypothesis and don't reject the null. I almost never think the null has a chance to be actually true so it's more a lack of evidence against the null than in any sense an acceptance that the null is the case. – Glen_b Jun 3 '13 at 1:53
• All this begs the questions of why we need formal hypotheses vs. estimating a quantity of interest and reporting confidence intervals. There is no bifurcation implied by estimation. – Frank Harrell Jul 15 '13 at 12:09

• That would be better, but there are still a lot that is left implicit, for instance H1 may not be the only alternative to H0 and the relative prior probabilities of H0 and H1 (which only really enter into the test indirectly via $\alpha$ and $\beta$) may be strongly against H0. The real problem is that we really want to know the probability that H0 is true, which a frequentist test can't give us, so it is a good idea to avoid terminology that could be interpreted that way, I like "fail to reject the null hypothesis" as it implies that its meaning is subtle (which it is!). – Dikran Marsupial Feb 19 '15 at 14:13