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Chi Square Sample Size

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  • #36902

    Ward
    Participant

    I am familiar with the requirment that expected values should be =>5 for each cell in chi square.  But can you have too large a sample size?  For instance:
          a     b     c            a            b           c
    A   10     9     11          1000     900      1100
    B     8     9       9              800     900       900
    P=.93   (fail to reject)                     p=.001 (reject)
    In each case the statistical decision will be different, although the proportions are the same.    Is there “a rule of thumb” to address too large a sample size?
    Thanks,
    Pete
     
     

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    #107633

    Jonathon Andell
    Participant

    Good question. Not my area of expertise, but my guess is probably not.
    However, in the instance below, it looks as if you have three Chi-Square categories (a, b, and c). If that is tue, then your Chi-square statistic has 3-1=2 degrees of freedom.
    Please correct me if I am wrong regarding my presumption.

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    #107635

    Mikel
    Member

    Not unique to the Chi square, sample size is like a lever. Long enough lever and you can flip over a Mack truck. Does that mean the truck is unstable?
    With a large enough sample size you can prove differences in anything. That is why you should have been taught to look for practical significance if you see statistical significance.

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    #107640

    Ang
    Participant

    Yes, you are correct.  In both instances, there are two degrees of freedom.

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    #107641

    Ward
    Participant

    Thanks Stan.
    I have never been a big fan of “rules of thumb” anyway.  It takes me 15 seconds to walk out to my mailbox.  If I were to construct a control chart, the purists would tell me I cannot establish control limits until I have 25-30 data points.  I would like to think I have a pretty good understanding of the process limits after just a few trips to the mailbox. Conversely, It may take more than 25-30 points for more complex or cyclical processes.   

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