Doubling the one-sided P-value in testing independence in 2 x 2 tables against a two-sided alternative

Dupont investigated the advantages of doubling the one-sided P-value in conducting a two-sided test of independence in a 2 x 2 table and claimed that the main advantage was that, unlike the 'exact' P-value, small changes in the table resulted in small changes in the significance. He admitted that this practice had no obvious theoretical justification. In this paper, I take the view that repeated sampling properties should form the basis of any such justification. I develop an appropriate framework for studying P-values and show that doubling the one-sided P-value produces a biased test whenever the table is asymmetric. I show how one may derive a slightly more complicated P-value from a uniformly most powerful test. While there are difficulties in interpreting these P-values, I argue that, in principle, one should prefer the latter. In practice the difference between the two is typically less than 10 per cent (for the tables Dupont considered, the difference is of the order of 1 per cent) but with highly skew tables the difference can be much larger.