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Categorical Data Analysis Using The SAS® System, 2nd Edition by Gary G. Koch, Charles S. Davis, Maura E. Stokes

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2.3. Exact Tests

Sometimes your data include small and zero cell counts. For example, consider the following data from a study on treatments for healing severe infections. A test treatment and a control are compared to determine whether the rates of favorable response are the same.

Table 2.3. Severe Infection Treatment Outcomes
TreatmentFavorableUnfavorableTotal
Test10212
Control246
Total12618

Obviously, the sample sizes requirements for the chi-square tests described in Section 2.2 are not met by these data. However, if you can consider the margins (12, 6, 12, 6) to be fixed, then you can assume that the data are distributed hypergeometrically and write

The row margins may be fixed by the treatment allocation process; that is, subjects are randomly ...

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