SUMMARYStatistical 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=β 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 paper the authors approach the problem from the more efficient viewpoint of the score method, which can be solved using a free program which is available from the webpage quoted in the article. In addition the paper 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.

Asymptotic inferences about a linear combination of K independent binomial proportions are very frequent in applied research. Nevertheless, until quite recently research had been focused almost exclusively on cases of K2 (particularly on cases of one proportion and the difference of two proportions). This article focuses on cases of K>2, which have recently begun to receive more attention due to their great practical interest.In order to make this inference, there are several procedures which have not been (which is a generalization of the Newcombe method). The article describes a new procedure (P0) based on the classic Peskun method, modifies the previous methods giving them continuity correction (methods S0c, W3c, N0c and P0c respectively) and, finally, a simulation is made to compare the eight aforementioned procedures (which are selected from a total of 32 possible methods). The conclusion reached is that S0c method is the best, although for very small samples (n i  10, i) the W3 method is better. The P0 method would be the optimal method if one needs a method which is almost never too liberal, but this entails using a method which is too conservative and which provides excessively wide confidence intervals. The W3 and P0 methods have the additional advantage of being very easy to apply.A free programme which allows the application of the S0 and S0c methods (which are the most complex) can be obtained at

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