Testing the homogeneity of small error rates: application to the sensitivity of different Elisa tests for aids antibodies

This note develops modifications of the chi-square and maximum likelihood tests for the homogeneity of the success probabilities pi of k binomial variables when the number of trials, ni, vary widely and all pi are small. With N = [Sigma]ni, and letting the ni/N approach fixed fractions, [gamma]i may differ. The procedures are appied to the first licensing data on the sensitivility which includes the case where the [gamma]i may differ. The procedures are applied to the first licensing data on the sensitivity of the ELISA tests used to screen for the AIDS virus and it is shown that one of the test kits was significantly less sensitive than the others.