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I have read some books in which Fisher's exact test will provide an exact p-value, but the assumptions underlying experimental design are not routinely met in practice. Apparently Fisher's "lady testing experiment" was specifically design to to meet the test requirements e.g. fixed number of poured milk before/after tea. I totally get this, but what I don't understand is why this condition is not met in other experimental designs? My intuition says that the number of rows/columns is controlled in every experiment...? I know there's something I am not quite getting, it'd be very useful if someone could provide an illustrative example for this.

Thanks!

Ramon Soto Garcia
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  • The claim is too strong; both margins don't have to be fixed. For example, it's pretty common that one margin is fixed and the other is not (in effect, comparing binomial proportions), but one need only condition on the margin that was not fixed in order to proceed with the exact test. The usual reasoning is that it is almost ancillary. However, people had been arguing all around the issue of conditioning on the margins in 2x2 tables (not just for the exact test) for many decades before I started studying statistics, and that was a long time ago now. Arguments about various issues continue – Glen_b Feb 05 '20 at 00:48

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