Simultaneous confidence interval for multiple proportions in R I want to perform in R the analysis "simultaneous confidence interval for multiple proportions", as illustrated in the article of Agresti et al. (2008) "Simultaneous confidence intervals for comparing binomial parameter", Biometrics 64, 1270-1275.
Unfortunately I did not succed to find any R example, and I have no idea how to implement this process in R.
As a case study, I need to apply such analysis on the following simple prolbem:
I did an experiment in which 12 participants had to choose between 3 conditions when provided with 3 stimuli.
Stimulus  Condition1  Condition2 Condition 3
A            9          1          2
B           10          2          0
C            8          2          2

I want to prove that it is not by chance that Condition 1 is preferred rather than the other two conditions. 
Can you please give me an example in R on how to perform such analysis?
In addition I would need to know how would you report such analysis in a paper.
Thanks in advance
 A: I just write a function for the Simultaneous Agresti-Caffo Confidence Interval based on Agresti et al. (2008) "Simultaneous confidence intervals for comparing binomial parameter", Biometrics 64, 1270-1275. I hope this helps
ac.sci = function (n1, x1, n2, x2, cl=0.95, k){
    p1 = x1/n1; p2 = x2/n2
    p1.tilde = (x1+1)/(n1+2)
    p2.tilde = (x2+1)/(n2+2)
    Q = qtukey(cl, nmeans=k, df=Inf)
    se = sqrt((p1.tilde*(1-p1.tilde)/(n1+2))+(p2.tilde*(1-p2.tilde)/(n2+2)))
    L = (p1.tilde-p2.tilde) - Q*se/sqrt(2)
    U = (p1.tilde-p2.tilde) + Q*se/sqrt(2)
    result = matrix(data=c(p1-p2, L, U), nrow=1, ncol=3)
    colnames(result) = c("Diff.P.hats", "Lower", "Upper")
    print(result)}

Example 1: Condition1 vs. Condition2 given A, where n1 = sum of Stimulus A + B + C of Condition1, and x1 = frequencies of Condition1 given Stimulus A. Similar to n2 and x2 for Condition2.
ac.sci(n1 = 27, x1 = 9, n2 = 5, x2 = 1, k=3)
the 95% CI = (-0.391, 0.509), since 95% CI contains 0 thus, we can conclude that Condition 1 is not statistically significant different from Condition 2 at a 5% level. 
Example2: A vs. B given conditions, where n1 = sum of conditions 1 + 2 + 3 of A, and x1 = frequencies of A given Condition1. Similar to n2 and x2 for B.
ac.sci(n1 = 12, x1 = 9, n2 = 10, x2 = 12, cl=0.95, k = 3)
the 95% CI = (-0.565, -0.172). Since 95% simultaneous Agresti-Caffo CI does not contain 0. Thus, we can conclude that A and B are different. 
