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Math Help - Type I versus Type II error

  1. #1
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    Type I versus Type II error

    A doctor found that therapy has an effect on reducing pain, but because of experimental error, the doctor's results led her to the conclusion that it has no significant effect. This is called:

    Type I error or Type II error?

    I have an explanation of the two types of errors (Type I-reject the null when shouldn't have; Type II- fail to reject the null when you should have), but I am having a hard time wrapping my brain around it.

    Would someone please be willing to explain to me in basic terms how I would figure this out?

    Thank you ahead of time!
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  2. #2
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    Re: Type I versus Type II error

    Hey vp1489.

    Basically a good way to think of it is that you have two distributions: one for each hypothesis.

    The Type I error is the probability region for the null hypothesis distribution that corresponds to your alpha significance value. Similarly the Type II error is the same thing, but its for the distribution for your alternative hypothesis.

    Each test statistic has a distribution and each hypothesis has a corresponding distribution for that particular test statistic.

    The distributions may be completely complementary (H0: mu = 0, H1: mu != 0) but they may not be (H0: mu = 0, H1: mu > 1). It depends on your specific hypothesis.

    That's it in a nutshell: get the hypothesis, find the test statistic, get its distribution and find the rejection region for each hypothesis distribution and that's your Type I and II errors.
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  3. #3
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    Re: Type I versus Type II error

    Thank you for taking the time to respond!

    The statement about the doctor is literally all of the information I am given for this particular problem and I need to determine if it is a Type I or II error (I am not given any data).

    Would you mind telling me if I am correct?
    I would say that it is a Type II error. The null would be that there was no effect from the therapy....therefore if the doctor's results led her to the conclusion that the therapy had no significant effect, she is failing to reject that null when she should have rejected it.

    Thanks again for your time.
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  4. #4
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    Re: Type I versus Type II error

    What hypothesis did they reject? H0 or H1?
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  5. #5
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    Re: Type I versus Type II error

    To be honest I am not completely sure (I'm sorry I have a teacher who isn't the greatest so I'm working my hardest to learn everything).

    I believe that the research hypothesis (which I think is H1?) is that the group who receives therapy would have reduced pain levels compared to the group who does not receive therapy.

    Knowing H1, I would assume that would mean that the null hypothesis would be H0 and it would be that there was no difference between the groups receiving therapy versus those who are not receiving therapy.
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  6. #6
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    Re: Type I versus Type II error

    If its H0 then its Type I, if its H1 its Type II. I can't help you figure out the hypothesis since I don't know anything about the experiment.
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