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Math Help - Relationship between t-test and Chi-squared

  1. #1
    Super Member Deadstar's Avatar
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    Relationship between t-test and Chi-squared

    This is something that has been pointed out to me but never explained. Any idea how these are linked? Heres the exact question...

    It is no accident that \Phi (1.96) = 0.975, i.e. z_{0.025} = 1.96, and  \chi^2_{0.05}(1) = 3.841 = (1.96)^2.

    Also

    It is no accident that  t_{0.025}(10) = 2.228, F_{0.05}(1,10) = 4.965 = (2.228)^2.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Deadstar View Post
    This is something that has been pointed out to me but never explained. Any idea how these are linked? Heres the exact question...

    It is no accident that \Phi (1.96) = 0.975, i.e. z_{0.025} = 1.96, and  \chi^2_{0.05}(1) = 3.841 = (1.96)^2.
    The square of a standard normal RV has a  \chi^2 distribution.

    Presumably the same relation holds for t and F distributions (but I do not know that).

    RonL
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