On the Comparison of Two Observed Frequencies

A significance measure essentially due to Liebermeister and dating back to 1877 may be preferable to Fisher's Exact Test, a conservative but commonly applied test when the sample sizes are small. We show that Liebermeister's measure is less conservative than Fisher's P-value and just as easy to calculate, while retaining the important features of a significance measure. We also compare Liebermeister's measure with Lancaster's mid-P, which has gained increasing acceptance as a replacement for Fisher's P-value. Application is made to a recent striking medical study on appendicitis symptoms for which the Fisher test does not give significance.