Inferences about a linear combination of proportions

Abstract

Statistical methods for carrying out asymptotic inferences (tests or confidence intervals) relative to one or two independent binomial proportions are very frequent. However, inferences about a linear combination of K independent proportions L = Σβ(i)p(i) (in which the first two are special cases) have had very little attention paid to them (focused exclusively on the classic Wald method). In this article the authors approach the problem from the more efficient viewpoint of the score method, which can be solved using a free programme, which is available from the webpage quoted in the article. In addition the article offers approximate formulas that are easy to calculate, gives a general proof of Agresti's heuristic method (consisting of adding a certain number of successes and failures to the original results before applying Wald's method) and, finally, it proves that the score method (which verifies the desirable properties of spatial and parametric convexity) is the best option in comparison with other methods.