HYPOTHESIS TESTING (ALPHA)

#1
Hi, In hypothesis testing we have the probability of type-1 error (alpha) and this area is called rejection region while the complementary area is called acceptance region. when the value of the test statistics falls in the rejection region we reject the null hypothesis But according to the definition of type-1 error (reject Ho when its true ) it says that Ho is true, then why do we reject Ho and accept the H1?
 

ondansetron

TS Contributor
#2
Alpha is the probability of rejecting the null hypothesis assuming (or when, given, if, all things that imply "in the circumstances that") that the null hypothesis is true-- this doesn't mean the null is true. It's just saying IF... THEN...but we don't know what is true.
 
#3
In statistical hypothesis testing, a type I error is the rejection of a true null hypothesis (also known as a "false positive" finding),---wikipedia
I am confused, why you used( assuming )
 

ondansetron

TS Contributor
#4
1) A type I error isn't a false positive, necessarily. If you look at it from the case that the null is true then rejecting the null may be viewed as a false positive, but the alternative is another perspective in that now that the null is rejected, is it a correct rejection (i.e. looking at all "positives" which were incorrect) which is a different perspective.
2) Saying "assuming the null is true, I reject it erroneously" is the same as saying "I incorrectly rejected the null" except in the former I'm recognizing that I don't know whether the null is true or not (and the latter I'm also saying I already rejected). It's really not much of a difference because it implies "in the case of a true null, rejecting the null is incorrect and labeled as a Type I error."