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

2.2. Chi-Square Statistics

Table 2.2 displays the generic 2 × 2 table, including row and column marginal totals.

Table 2.2. 2 × 2 Contingency Table

Column Levels	Row Levels
	1	2	Total
1	n11	n12	n1+
2	n21	n22	n2+
Total	n+1	n+2	n

Under the randomization framework that produced Table 2.1, the row marginal totals n₁₊ and n₂₊ are fixed since 60 patients were randomly allocated to one of the treatment groups and 64 to the other. The column marginal totals can be regarded as fixed under the null hypothesis of no treatment difference for each patient. Then, given that all of the marginal totals n₁₊, n₂₊, n₊₁, and n₊₂ are fixed under the null hypothesis, the probability distribution from the randomized allocation of patients to treatment can be written

which is ...