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    Hi,

    I would like to clarify a few things regarding the chi-squared distribution:

    1. Why are there 2 different equations for the chi-squared statistic?

    



\chi^2 = \sum\frac{(x - \bar{x})^2}{\sigma^2}



\chi^2 = \sum\frac{(O - E)^2}{E }

    Each equation is used under what circumstances?

    2. For degree of freedom, I read that it is the difference between number of classes and number of constraints. Could anyone explain the term 'constraint' in a more detailed manner?

    Thanks!
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    Hi, pls help me out in this qn! Thanks
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    (Original post by superkinetic)
    Hi,

    I would like to clarify a few things regarding the chi-squared distribution:

    1. Why are there 2 different equations for the chi-squared statistic?

    



\chi^2 = \sum\frac{(x - \bar{x})^2}{\sigma^2}



\chi^2 = \sum\frac{(O - E)^2}{E }

    Each equation is used under what circumstances?

    2. For degree of freedom, I read that it is the difference between number of classes and number of constraints. Could anyone explain the term 'constraint' in a more detailed manner?

    Thanks!
    \displaystyle \chi^2 = \sum\frac{(O_i - E_i)^2}{E_i} is the general formula for the Pearson chi-square test.

    \displaystyle \chi^2 = \sum\frac{(x - \bar{x})^2}{\sigma^2} is used when we have a Binomial approximation to the Normal, and has 1 degree of freedom.

    In terms of constraints and degrees of freedom, this is what my notes say:
    The ‘degrees of freedom’ tells us which row of the chi-square table to use. WM&S, Section 14.3, suggest the number of cells, less 1 as the Ei add up to a fixed n, ....less the number of estimated parameters. This is not quite correct, unless the parameters are estimated from the cell frequencies Oi. If they are estimated from the original data, the degrees of freedom lie between ‘number of cells less one’, and ‘number of cells less one and less number of parameters estimated’.
 
 
 
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