8.41.* Table 8.30 exhibits the maximum possible association between two binary variables for a sample of size n.

(a) Show that X2 = n for this table and, hence, that the maximum value of X2 for 2 × 2 tables is n.

(b) The phi-squared measure of association for 2×2 contingency tables has sample value

ˆφ

2 = X2 n

.

Explain why this measure falls between 0 and 1, with a population value of 0 corresponding to independence. (It is a special case, for 2 × 2 tables, of the r2 measure introduced in the next chapter.)

TABLE 8.30 n/2 0 0 n/2