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  • 1.  Chi sq test of independent

    Posted 08-16-2017 13:39
    Can the chi square test of independence in a 2x2 contingency table test whether or not the sample used to test independence is random or not?

    It would seem odd if it could since the chi-sq test requires a random sample in the first place.

    Thank you for your response.

    Paul


  • 2.  RE: Chi sq test of independent

    Posted 08-17-2017 08:01

    I would say no, because the main effect of non-randomness of sample selection would be that your sample is different from the rest of the population from which it comes. You cannot assess that by looking within a sample, only by a comparison to the population.


    Ed


    Ed J. Gracely, PhD
    Associate Professor
    Family, Community, & Preventive Medicine
    College of Medicine

    Associate Professor
    Epidemiology and Biostatistics
    Dornsife School of Public Health

    Drexel University
    2900 W. Queen Lane,
    Philadelphia PA, 19129
    Tel: 215.991.8466      | Fax: 215.843.6028
    Cell: 609.707.6965
    eg26@drexel.edu (egracely@drexelmed.edu forwards)
    drexelmed.edu  |  drexel.edu/publichealth




    Original Message


  • 3.  RE: Chi sq test of independent

    Posted 08-17-2017 11:37
    CHI squared test is to test if the row variable A (categories) dependent from the col variable B (categories).  To see if compared to group A2, people in group A1 is more possible to be in group B1.

    The random sample requirement for the test has a different meaning from that. It mainly about the sampling process: each one from the population has the same possibility to be selected; the fact that point1 has been selected doesn't change the possibility point2 will be selected.

    If you have time for reading more, text books have more accurate definitions about these.   

    Thanks

    Yujiao Mai





    Original Message


  • 4.  RE: Chi sq test of independent

    Posted 08-17-2017 12:39
    A sample is random if it is selected randomly from the population. There is no way to tell if a sample was selected randomly by examining the sample. Properties of a given sample may be unusual (rare) in random samples but that is always true for some properties.

    ------------------------------
    Chauncey Dayton
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    Original Message


  • 5.  RE: Chi sq test of independent

    Posted 08-17-2017 15:00
    Paul,


    You're right it's implicit in the null hypothesis for the test that sampling was random. (Explicitly the null hypothesis is about the independence of the variables that have been properly randomly sampled.)


    I'd suppose one could attempt a "modus tolens" type of logic, but it would be a stretch: If it's (independently) believed that the variables are independent, then if a random sample is taken then you'd expect not to find significance. If the test finds significance (i.e. "refutes the consequent"), is this evidence that the randomness assumption was false? ....or is it evidence that the variables are not independent after all? I don't think one simple chi-square test can address all this at once.


    Bill


    Original Message


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