Expected frequencies: Compute the expected frequencies under the null hypothesis of homogeneity.

In a hypothetical study, four hospitals were compared with regard to the outcome of a particular type of surgery. For each patient at each hospital, the outcome was classified as Substantial improvement, Some improvement, or No improvement.
The results are presented in the following contingency table.

Outcome Substantial Some No Hospital Improvement Improvement Improvement A 114 64 22 BCD 132 52 16 100 64 36 D 126 56 18