Exact unconditional non-classical tests on the difference of two proportions

The paper analyzes the three possible unconditional exact tests on the difference (d = p(2) - p(1)) of two independent binomial proportions: H-SG: d less than or equal to delta vs. K-SG: d > delta,H-PEG: d is not an element of (delta(1), delta(2)) vs. K-PEG: d is an element of [delta(1,) delta(2)] and H-SDG: d is an element of [delta(1,) delta(2)] vs. K-SDG:d is not an element of [delta(1), delta(2)], where H(K) refers to the null (alternative) hypothesis. For this purpose the methodological bases of such tests are established; the properties of convexity and symmetry of the classic statistic z-pooled are studied; and, finally, the article indicates how to reduce computing problems by decreasing the parametric space and sample space involved (which can reduce the computing time up to tenfold). These tests are a generalization of the classic case (delta = 0 in SG; delta(1) = delta(2) = 0 in SDG) and the non-classic case (delta < 0 in SG for establishing non-inferiority; delta > 0 in SG for establishing substantial superiority; delta(2) = -delta(1) > 0 in PEG for establishing equivalence). The paper also proves that the present test PEG is more powerful than the one based on the classic TOST (two one-sided tests) method. Finally, the above tests were used to obtain exact confidence intervals. (C) 2002 Elsevier B.V. All rights reserved.