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 LevelsRow Levels 
12Total
1n11n12n1+
2n21n22n2+
Totaln+1n+2n

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 ...

Get Categorical Data Analysis Using The SAS® System, 2nd Edition now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.