3.32 For testing independence, show that X2 ≤ n min(I – 1, J-1). Hence V2 =

X2/[n min(I - 1, J - 1)] falls between 0 and 1 (Cramér 1946). [For 2 x 2 tables, X2/n is often called phi-squared; it equals Goodman and Kruskal's tau of Exercise 2.39. Other measures based on X2 include the contingency coefficient

[X2/(X² + n)]1/2, which Pearson (1904) proposed as an estimate of the correlation for an underlying bivariate normal distribution.]