Optimal unconditional critical regions for 2 2 2 multinomial trials

Analysing a 2 2 2 table is one of the most frequent problems in applied research (particularly in epidemiology). When the table arises from a 2 2 2 multinomial trial (or the case of double dichotomy), the appropriate test for independence is an unconditional one, like those of Barnard (1947), which, although they date from a long time ago, have not been developed (because of computational problems) until the last ten years. Among the different possible versions, the optimal (Martin Andres & Tapia Garcia, 1999) is Barnard's original one, but the calculation time (even today) is excessive. This paper offers critical region tables for that version, which behave well compared to those of Shuster (1992). The tables are of particular use for researchers wishing to obtain significant results for very small sample sizes (N h 50).