Confidence intervals for the mean of a variable taking the values 0,1 and 2

The problem of setting a confidence interval for the mean of a variable on (0, 1,2) arises in three contexts: paired organ procedure rates; estimation of gene frequency, and three-point Likert scales. An effective approach to its estimation may be based on a good interval for a paired difference of proportions. Four good methods due to Newcombe and Tango are shown to have much better performance than more naive methods over regions of the parameter space corresponding to the above applications.