Sample sizes for the exact test of 'no interaction' in 2 X 2 X 2 tables

The exact two-sided test of the hypothesis of 'no interaction' in a 2 X 2 X 2 table with fixed totals of rows X columns is considered. A method of approximating the power of the test, based on the limiting conditional distribution of a cell entry (Godambe and Harkness, 1975, Communications in Statistics 4, 699-709), is introduced and found to provide a close fit. This method can be utilized to calculate the sample sizes required to detect interaction effects with a pregiven power.