Thread: Accepting the null hypothesis?

Is it possible to even accept the null hypothesis? In introductory stats course I was taught that that null is never accepted, but rather we fail to reject it (this was done for tests absed only on p-values.) However, in a Mathematical Statistics course I took (we used Introduction to Mathematical Statistics by Hogg, McKean, Craig) the text often talked about accepting the null. In online resources, I see differing opinions. I've read that the null is never accepted, and I've also read that it can be accepted if you "accrue" enough evidence in support of it, either through confidence intervals or power functions - source: http://w3.sista.arizona.edu/~cohen/P...ohenIEEE96.pdf

"It is important to understand that the null hypothesis can never be proven. A set of data can only reject a null hypothesis or fail to reject it. For example, if comparison of two groups (e.g.: treatment, no treatment) reveals no statistically significant difference between the two, it does not mean that there is no difference in reality. It only means that there is not enough evidence to reject the null hypothesis (in other words, the experiment fails to reject the null hypothesis)."

Taken from Null hypothesis - Wikipedia, the free encyclopedia

Yes, I am aware of the Wikipedia definition of null hypothesis. I agree that in tests based solely on the p-value, one can never accept the null hypothesis. However, I've read several papers/books which discuss conditions under which the null hypothesis can indeed be accepted. One of those sources was linked in the OP. Such as 'Intro to Mathematical Statistics' by Hogg, McKean, Craig, and 'Statistical Power Analysis for the Behavioral Sciences' by Cohen.

ive always assumed that you can deduce that the null null hypothesis is true if you can identify every possible alternative and reject it; but that is based on no official source whatsoever.

eg, if suppose X is normal with unknown mean, but that the mean is definately 0 or 100. if there is enough evidence to reject 100, i would "accept" 0. but in practice this hardly ever happens...

I think its just the terminology used. When you choose null hypothesis you also have the opposite hypothesis - alternative or research hypothesis. When you reject the null hypothesis this implies that you accept the alternative. Or when you fail to reject the null hypothesis then one can speak of accepting the null hypothesis - or rejecting the research hypothesis.
I'll say it again - I think its just the terminology used. Fail to reject = accept?! Still, I might be wrong, its just that I don't see how.

The only way you can accept the null hypothesis is if you perform a census of the population about which the null hypothesis is concerned. E.g. if the null hypothesis claims that "All swans are white" you would have to investigate all past, present and future swans and note their colour; of course, in this case it is impossible to accept the null hypothesis.