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I have read that the degree of freedom is calculated by subtracting 1 from the number of states a random variable can be in. I am performing a goodness of fit test on a 64*32 strict avalanche criterion matrix where the expected frequency of any a[i,j] is 50000 and the observed frequency can lie between [0,100000].What I am confused about is that how do I calculate the degree of freedom? Since the observed value might range from 0-100000, will my degree of freedom be equal to (100000-1)? Please advise.

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you have $n=64\times 32$ random variables so your degrees of freedom should be $n-1=2047.$

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  • $\begingroup$ But I have a new problem,I have getting chi-squared statistic in the order of 10^7 and p-value as 0 $\endgroup$ – Kishan Kishore Apr 9 '16 at 18:53
  • $\begingroup$ Maybe raw chi squared is not the way to go. On page 23 of the document cosic.esat.kuleuven.be/nessie/deliverables/… a normalized measure is used for a similar purpose. So try to scale your random variables to be X_{i,j}=|(a[i,j]/#X)-1| where #X is 64 and then apply chi squared to the sum of these normalized variables. $\endgroup$ – kodlu Apr 10 '16 at 0:27

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