3.30 Show that x2 = n ; ; (Pij - Pi+P+j)/Pi+P+j = n ; Pi+P+j (aij - 1)2 for the sample association factors {aij}.

3.30 Show that x2 = n Σ; Σ; (Pij - Pi+P+j)²/Pi+P+j = n Σ₁ Σ; Pi+P+j (aij - 1)2 for the sample association factors {aij}. Thus, X2 can be large when n is large, regardless of whether the association is practically important. Explain why this test, like other tests, merely indicates the degree of evidence against Ho and does not describe strength of association. ("Like fire, the chi-square test is an excellent servant and a bad master," Sir Austin Bradford Hill, Proc. R. Soc. Med. 58: 295-300, 1965.)