Dear listers,
I have no question about the derivation of Expectation and Variance for
1x2 case (finite population with 2 classes) of hypergeometric
distribution. However, when the problem is augemented to 2x2 case, I have
no clue to find its Expected value and Variance. Suppose we have the
following 2x2 contingency table:
Row Level
Col. 1 2 Total
1 n11 n12 n1.
2 n21 n22 n2.
Total n.1 n.2 n
Where nij is the number for cell{i, j}, n is the total number (the finite
population). I have no problem in representing the probability for nij,
since
P(nij) = C(n1., n11) x C(n2., n21)/ C(n, n.1)
= n1.! n2.! n.1! n.2! / (n! n11! n12! n21! n22!).
Interestingly, it seems that the probability for each cell is the same,
since P(nij) does not depend on i or j. So I feel strange how one can
derive its corresponding expectation and variance? My book shows
E{nij|H0} = ni. n.j/n
V{nij|H0} = n1. n2. n.1 n.2 / (n^2 (n-1)),
where H0 is the condition that there is no association between row and
column.
Could someone give me a hint?
Wen-Feng
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