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Math Help - Chi square distribution

  1. #1
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    Chi square distribution

    If we want to evaluate P(chi square with n degrees of freedom>=k)=0.05

    should I say k=chi square(n,0.05) or k=chi square (n, 1-0.05)?

    I am not sure since I don't know if >= or <= makes a difference in chi square distribution as it does in normal distribution (which is symmetric), but chi square is not!

    Any help would be appreciated, thank you
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  2. #2
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    Re: Chi square distribution

    Quote Originally Posted by Darkprince View Post

    I am not sure since I don't know if >= or <= makes a difference in chi square distribution as it does in normal distribution (which is symmetric), but chi square is not!
    You are correct to say \chi^2 is not symmetric.

    Your 0.05 value is a probability, the region under the curve. The left hand critical value which gives p=0.05 (region under the curve) will be different to the critical value for the right hand side p= 0.05
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  3. #3
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    Re: Chi square distribution

    Quote Originally Posted by pickslides View Post
    You are correct to say \chi^2 is not symmetric.

    Your 0.05 value is a probability, the region under the curve. The left hand critical value which gives p=0.05 (region under the curve) will be different to the critical value for the right hand side p= 0.05

    So which value I should use? k=chi square(n,0.05) or k=chi square(n,0.95)?

    If I had to evaluate P(chi square with n degrees of freedom<=k)=0.05 would it be different, obviously, but how do I know which value I take each time?
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  4. #4
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    Re: Chi square distribution

    Depends on the table/technology you are using.

    To find a critical value, let's say df=15

    In ms-excel
    CHIINV(0.95,15) = 7.26 (left tail)
    CHIINV(0.05,15) = 25.00 (right tail)

    Draw a picture of the curve with these values on it, does it help?
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  5. #5
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    Re: Chi square distribution

    Quote Originally Posted by pickslides View Post
    Depends on the table/technology you are using.

    To find a critical value, let's say df=15

    In ms-excel
    CHIINV(0.95,15) = 7.26 (left tail)
    CHIINV(0.05,15) = 25.00 (right tail)

    Draw a picture of the curve with these values on it, does it help?

    Basically I have the following (which is a part from a problem I solved):

    Under Ho (null hypothesis)
    P(Sum from i=1 to 50 of Xi >= k) = P(Sum from i=1 to 50 of 4*Xi >=4k) = P(chi square with 200 df >= 4k) since I had deduced in the problem that the sum follows that distribution.

    But at the same time P(Sum from i=1 to 50 of Xi >=k) = 0.05 (0.05 is the power of my test)

    The problem had to do with most powerful test and region. The thing is that P(Sum from i=1 to 50 of Xi >=k) = 0.05 if and only if 4k = chi square with 200 df but looking at 0.05 or 0.95? This was my question!

    If I had P(Sum from i=1 to 50 of Xi <= k) = 0.05 it would be a different case? So this is my question, if my sum >=k or my sum <=k would change the value of chi square with 200 df I should look in my tables.

    I hope I got clear this time with my question

    In my problem I have the sum >=k, not <=k!
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