A numerical comparison of several unconditional exact tests in problems of equivalence based on the difference of proportions

In order to compare two independent proportions (p(1) and p(2)) there are several useful tests for the parameter d = p(2) - p(1) : H-SG : d <= delta vs. K-SG : d > delta, H-SG2 : d = delta vs. K-SG2 : d not equal delta (where -1 < delta < +1), H-SD : vertical bar d vertical bar <= Delta vs. K-SD : vertical bar d vertical bar > Delta (where Delta >= 0) and H-PE : vertical bar d vertical bar >= Delta vs. K-PE : vertical bar d vertical bar < Delta (where Delta > 0). The exact unconditional test requires an ordering statistic, which is usually the z-pooled statistic, to be defined. The paper gives the definition of 10 new ordering statistics with a similar computational time, and compares the number of points which each introduces into the critical region obtained to error alpha = 5%. The article reaches the conclusion that the most generally powerful statistics are: the z-pooled one with a small continuity correction (c = 1/N if n(1) not equal n(2) or c = 2/N if n(1) = n(2), where N = {n(1)+1} {n(2) +1} and n(i) are the sample sizes) and those z-pooled with Yates' continuity correction (c = {n(1) +n(2)}/{2n(1)n(2)}). In this paper the author also showed that Barnard's two classic convexity conditions are redundant, because when one of them is verified the other is also verified. The programs for these tests may be obtained free of charge from the site http://www.ugr.es/local/bioest/software.htm.