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### 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
YesNoTotalProportion Yes
Group 1n11n12n1+p1 = n11/n1+
Group 2n21n22n2+p2 = n21/n2+
Totaln+1n+2n

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 ...

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