Confidence intervals and sample sizes for multinomial data

Abstract

This paper surveys the existing literature on confidence intervals for multinomial data. Multinomial situations (fractions) are very common as is illustrated in medicine and information sciences. Only conservative results exist. We make a comparison of several results and select the best confidence intervals. We show that, in general, the simplest methods perform best(such as the methods derived from the central limit theorem and the Bonferroni inequality). We also show that the method of Fitzpatrick and Scott cannot be the best for all fractions involved(al least if there are more than two classes). The sample sizes are derived from the formulae of the confidence intervals. Fixed length intervals as well as proportional lenghts are considered.. It is found that for only estimating the highest proportions in an accurate way, the sample sizes are reasonable and well-applicable. The paper closes with improved confidence intervals in the case they are dependent on the proportions and with some practical conclusions.