The StatXact manual gives a formula for the empirical odds ratio which is the inverse of what is found in Agrestis An Introduction to Categorical Analysis. Can you explain this inconsistency?
A. StatXact’s formula for the empirical odds ratio is consistent with StatXact’s formula for the true odds ratio. We recognize that some textbooks use the reciprocal of our definition for the odds ratio in a 2×2 table. That is, whereas we use column 1 as the un-exposed group and column 2 as the exposed group, they might use column 1 as the exposed group and column 2 as the un-exposed group. Either convention is ok. As long as one is consistent with the definition and enters the data appropriately into the table, there should be no confusion. We prefer our definition because it extends in a natural way to ordered 2xc tables. In these tables, column 1 is once again the unexposed group and columns 2, 3, 4 … represent progressively greater exposures relative to column 1.
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