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Math Help - What exactly is a Type II Error

  1. #1
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    What exactly is a Type II Error

    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.
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  2. #2
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    Quote Originally Posted by alan4cult View Post
    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.
    If you Google Type 2 Error you will get very clear answers. The definition is very clear.
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    If you Google Type 2 Error you will get very clear answers. The definition is very clear.
    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?
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  4. #4
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    Quote Originally Posted by alan4cult View Post
    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.
    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).

    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?
    Exactly what is not clear about:



    which has been cliped straight from the Wikipedia article on type I and II errors.

    CB
    Last edited by CaptainBlack; May 8th 2009 at 11:46 PM.
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  5. #5
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    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.
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  6. #6
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    Quote Originally Posted by alan4cult View Post
    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
    Last edited by CaptainBlack; May 9th 2009 at 06:20 AM.
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  7. #7
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    Ok so if I can't reject the null I must accept it then?
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  8. #8
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    Quote Originally Posted by alan4cult View Post
    Ok so if I can't reject the null I must accept it then?
    That is the way such problems are formulated.

    CB
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  9. #9
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    Quote Originally Posted by mr fantastic View Post
    If you Google Type 2 Error you will get very clear answers. The definition is very clear.
    Quote Originally Posted by CaptainBlack View Post
    That is the way such problems are formulated.

    CB
    Thanks very much for all your help!
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