Exact unconditional non-classical tests on the difference of two proportions ?
The paper analyzes the three possible unconditional exact tests on the difference (d=p2?p1) of two independent binomial proportions: vs. vs. and vs. KSDG:d?[?1,?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 (?=0 in SG; ?1=?2=0 in SDG) and the non-classic case (? 0 in SG for establishing substantial superiority; ?2=??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.
difference of two proportions exact tests superiority equivalence exact confidence intervals non-inferiority unconditional tests 22 tables