In the non-comprehensive models at least one of the variables is not used. We show how to calculate the expected frequencies for one such model, namely (*A, B*). The degrees of freedom are *abc* – (*a* – 1) – (*b* – 1) –1 = *abc – a – b* + 1.

Figure 1 displays the expected frequencies for this model for the data in Example 1 of Three-way Contingency Tables.

**Figure 1 – Expected frequencies for ( C, T) model**

For example the expected frequency of a positive result for males taking therapy 1 (cell J74) is calculated via the formula =M80*J78/(COUNTA(I83:I84)*M78). The degrees of freedom for this model is 2 ∙ 2 ∙ 3 – 2 – 3 + 1 = 8. χ^{2} (maximum likelihood) is 65.13 with 8 degrees of freedom, which is significant, and so this model is not a good fit for the data.