In continuation of the authors' tables of significance tests (1963), the power function of this exact test for the 2 × 3 contingency table using the Freeman & Halton principle is derived and evaluated numerically in the form of contours of constant power for the cases:A= 5(5) 15, whereAis the total number in each of the three groups observed according to the numbers of ‘Successes’ (= ai) in each. Comparisons are also made with the exact significance points of the competingX2and (−2 log λ) tests under the null hypothesisH0and also alternatives toH0.