Large Sample Simultaneous Confidence Intervals for the Multinomial Probabilities Based on Transformations of the Cell Frequencies

The paper outlines a detailed study of three sets of large sample simultaneous confidence intervals for the probabilities of a multinomial distribution, all three making use of the Bonferroni inequality. One of them, originally proposed by Goodman, is based on the assumption that each cell frequency n i is, marginally, normally distributed, while the other two require the normality of transformations of n i -an angular transformation in one case and a square root in the other. It is shown that all three sets of intervals should be used with a correction for continuity; their coverage probabilities are investigated, and it is seen that the two sets based on transformations of n i produce shorter intervals than Goodman's when n i is small. There is little to choose between these two except that one of them is a little simpler to use than the other.