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Help on Statistics problem!

  1. Feb 16, 2006 #1
    Heres the problem:

    When asked to explain the meaning of "statistically significant at the 0.05 level," a student says, "This means there is only probability 0.05 that the null hypothesis is true." Is this an essentially correct explanation of statistical significance? Explain.


    Help please. Appreciated.
     
  2. jcsd
  3. Feb 16, 2006 #2
    More specifically, it is the probability that you reject a true null hypothesis.

    The difference in the statements is subtle.

    The probability of the null hypothesis being true may be 20%, 50%, etc. -- but the probability of rejecting it is .05.
     
  4. Feb 16, 2006 #3

    0rthodontist

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    Well, you can't say anything about the probability of the null hypothesis being 20% or 50% right off the bat because probability is based on the amount of knowledge you have. For one person the probability of the null hypothesis being true might be 20% and for another person with more knowledge the probability of the same hypothesis being true might be 1.

    But if the probability of a type I error is the probability that the null hypothesis is true and you reject it, then let A = the null hypothesis is true and let B = you reject the null hypothesis.
    Then P(A n B) is the probability of a type I error, and P(A n B) = .05
    But you know that P(B) = 1 since the test was significant. So P(A n B) = P(A) = .05 and the probability that the null hypothesis is true is .05.
     
  5. Feb 17, 2006 #4

    EnumaElish

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    Is this homework? If it is, it is not supposed to have been posted here. If it is not HW, why did you post it under HW help?
     
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