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Why does Chi-square formula have two different ones?

  1. Oct 3, 2011 #1
    One is:

    where at the bottom of the page, chi-square = sum of something devided by variance.

    However, here:
    http://www.napce.org/documents/research-design-yount/23_chisq_4th.pdf [Broken]

    where the chi-square formula is that the sum of the same thing devided by expectation value.

    Which formula is right then?
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Oct 4, 2011 #2


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    Science Advisor

    The first reference is the definition of Chi-squared :- the distribution of a RV formed from the sum of squared standard-normal random variables.

    The second reference is an application of the above distribution to the case of expect versus observed frequencies, where (O-E)/sqrt(E) is asymptotically standard-normal and hence (O-E)^2/E is asymptotically Chi-squared.
  4. Oct 4, 2011 #3

    It seems that for goodness of fit I should use the second formula to either reject or accept the null hypothesis, rather than use the first formula.
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