SIMULTANEOUS CONFIDENCE INTERVALS FOR MULTINOMIAL PROPORTIONS, THEIR DIFFERENCES AND RATIOS

Estimation of simultaneous confidence intervals for multinomial proportions, their differences and ratios is a long-standing problem in the literature. Existing methods suffer either from enforced symmetry and/or conservative coverage. We propose calculating confidence limits using the Wilson method or Jeffrey’s procedure for the multinomial proportions and for ratios of multinomial proportions with critical values obtained from multivariate normal distributions that accounts for correlations among proportions and contrasts. Confidence intervals for the contrasts are then obtained by recovering variance estimates from limits for single proportions. Simulation study shows that proposed methods perform well for a variety of parameter combinations. Data on mutational damage in Saccharomyces cereυisiae is used to illustrate the procedures.