An exact method of testing equality of several binomial proportions to a specified standard

The problem of testing equality of several binomial proportions to a speci)ed standard is considered. An exact method of testing based on the test statistic considered in Kulkarni and Shah (Statist. Probab. Lett. 25 (1995) 213) is proposed. Exact properties of the exact method and the approximate method due to Kulkarni and Shah are evaluated numerically for the two-sample case. Numerical studies show that the sizes of the approximate test due to Kulkarni and Shah often exceed the nominal level by considerable amount. For the one-sample case, numerical comparison shows that there is no clear cut winner between the new test and the usual exact test. A procedure for constructing simultaneous con)dence intervals is also given. The methods are illustrated using two examples. c © 2003 Elsevier B.V. All rights reserved.