Testing the equality of several binomial proportions to a prespecified standard

Abstract

Testing the equality of several binomial proportions was first proposed by Pearson (1900) and the discussion of this test can be found in standard statistics books. In this article we consider testing the equality of several binomial proportions to a known standard. For testing such a hypothesis against a two sided alternative, an intuitive test statistic and its null distribution have been mentioned in Rohatgi (1976). Here we study the non-null distribution of that statistic and provide a simple way of calculating the approximate power via a moment approximation method (MAM). A procedure of constructing simultaneous confidence intervals is also given here. Additionally, we propose test statistics for testing the above null hypothesis against one sided alternative hypotheses. We give simple methods of obtaining the p-value and the power for these test statistics. Finally, two examples are given to illustrate the techniques.Homogeneity of binomial proportions Moment approximation