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 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.
difference of two proportions exact tests superiority equivalence exact confidence intervals non-inferiority unconditional tests 2 x 2 tables