I'm wondering what is the actual definition of a Type 2 Error?
For example:
In a hypothesis test, if I fail to reject the null hypothesis this is clearly not the same as accepting the null hypothesis. I am merely saying that I don't have enough evidence to say the null hypothesis is not true.
"Absence of evidence is not evidence of absence".
The question I ask is when is a type 2 error committed?
Is it committed when I fail to reject the null hypothesis or is it committed when I accept the null hypotheis or could it even be that both situations are true?
Thanks.
I don't think they are very clear.
I think that failing to reject the null hypothesis is not the same as accepting the null hypothesis.
I think the only possible time you can commit a type 2 error is when you accept the null hypothesis.
I'm just wondering is it possible to commit a type 2 error when I fail to reject the null hypothesis?
You have a decision problem, the allowable outcomes are accept the null hypothesis or reject the null hypothesis. So failing to reject is the same outcome as accepting the null hypothesis (this is not colloquial English in use here where there may be some ambuigity).
Exactly what is not clear about:I think the only possible time you can commit a type 2 error is when you accept the null hypothesis.
I'm just wondering is it possible to commit a type 2 error when I fail to reject the null hypothesis?
which has been cliped straight from the Wikipedia article on type I and II errors.
CB
But failing to reject is not the same as accepting.
EXAMPLE - Court Case
Null Hypothesis - Innocent
Alternative Hypothesis - Guilty
If you fail to reject the null that does not mean I'm innocent it just means you cannot say I'm guilty beyond a reasonable doubt. So in a sense I'm "not guilty" which is different from being innocent.
Law courts accept just two verdicts Guilty and Not Guilty (in England at least).
But that is irrelevant anyway the decision problem that is involved is what I gave earlier, not whatever you think it may mean. You are either going to accept te null hypothesis or reject it. If you want a third choice, then you are addressing a different problem with a different procedure.
CB