Categorical Data Analysis Using The SAS® System, 2nd Edition

2.4. Difference in Proportions

The previous sections have addressed the question of whether there is an association between the rows and columns of a 2 × 2 table. In addition, you may be interested in describing the association in the table. For example, once you have established that the proportions computed from a table are different, you may want to estimate their difference.

Consider the following table, which displays data from two independent groups:

Table 2.5. 2 × 2 Contingency Table

	Yes	No	Total	Proportion Yes
Group 1	n11	n12	n1+	p1 = n11/n1+
Group 2	n21	n22	n2+	p2 = n21/n2+
Total	n+1	n+2	n

If the two groups are simple random samples from populations with corresponding probabilities Yes denoted as π₁ and π₂, you may be interested in estimating the ...