Rule of thumb for log-linear analysis


I am analysing categorical data using hierarchical log-linear analysis; I have 3 binary variables. The books I have consulted suggest that before I proceed with the analysis, I examine expected cell frequencies when the data are cross-tabulated; less than 20% of cells should have expected frequencies less than 5, otherwise the power of the test may be reduced.

However I am confused about how to compute the total number of cells: if I cross-tabulate two of the variables with the third as a layer (as suggested by Field 2005), than I have a total of 8 cells, while if I examine all two-way associations (as suggested by Tabachnick & Fidell 1996), then I have a total of 12 cells. This means that I can have either 1.6 or 2.4 cells with expected frequencies less than 5. I know this is somewhat of a trivial question, however it does affect how I code the data.

Many thanks!