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Math Help - Type 1 and Type 2 Errors

  1. #1
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    Joined
    Aug 2009
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    Type 1 and Type 2 Errors

    Hello,

    I was given the following handout:

    Study design:

    Alpha = 0.05
    Effect size = 0.3
    Sample size n = 40

    From these figures we can compute that:

    Beta = 0.40
    Power = 0.60
    I know how to get the power, because this is 1 - beta = 1 - .40 = .60. But I just don't get how beta was calculated using the above figures.

    Plus, if I have the following problem:

    A sample size of 102 will be sufficient to detect an effect size of 0.5 with 80% power at the 0.05 level of significance.

    a) What are the type 1 and type 2 error rates?

    To get the type 1 error do I look at the alpha, which in this case is 0.05? Therefore, the probability of a Type 1 error = 5% ?

    To get the type 2 error is it 1 - Power?

    I think that I need to know the value of beta to determine my type 2 error? But I just don't understand how to get beta.

    I'd be ever so grateful if someone could explain to me how I'd manage to calculate my type 2 error.
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  2. #2
    Member
    Joined
    May 2011
    From
    Sacramento, CA
    Posts
    165
    With the three pieces of information, you can always determine one of the other two provided (though, really one piece of information. The power of the test just is 1 - beta). I suggest reading up on the power of a test (an important concept in study designs). Wikipedia is a good place to start.

    As for the type of errors, look up what type 1 and type 2 errors mean and the definitions of \alpha and \beta. You'll see a profound similarity
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