Fisher exact test is one of most popularly used methods in modern data analyses. However, it is conservative because of discreteness. The mid-p method may reduce the conservativeness but it is defined by the factor 1/2, an extra term beyond data. This paper considers an adjustment defined by a data-based factor. The adjusted test is compared with other ten tests. Special attention is given to the comparison between the data-based factor and the factor 1/2. The standardized version of the adjusted test is asymptotically
standard normal.
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