Let the observations aij, (i=1,2:j =1,2,……, k) be arranged in a 2 x k contingency table as follows:
A | A1 | A2 | ………… | Ai | ……………. | Ak | Total |
B1 | a11 | a12 | ………… | a1i | ……………. | a1k | m1 |
B2 | a21 | a22 | ………… | a2i | ……………. | a2k | m2 |
Total | n1 | n2 | ………… | ni | ……………. | nk | N |
Under the hypothesis of independence of attributes, we have
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