Dear list members,
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.
If I am not wrong the R function implementing the Agresti et al. method is
prop.test(). I ask an help because I have some difficulties in reading the
output of that function.
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
My goal is to prove that it is not by chance that Condition 1 is preferred
rather than the other two conditions.
So, I apply the function prop.test(), summing the values of Conditions 2 and 3):
table<-matrix(c(9,3,10,2,8,4),ncol=2,byrow=T)
rownames(table)<-c("stimulusA","stimulusB","stimulusC")
colnames(table)<-c("Condition1","Conditions2and3")
> table
Condition1 Conditions2and3
stimulusA 9 3
stimulusB 10 2
stimulusC 8 4
prop.test(table)
> prop.test(table)
3-sample test for equality of proportions without continuity correction
data: table
X-squared = 0.8889, df = 2, p-value = 0.6412
alternative hypothesis: two.sided
sample estimates:
prop 1 prop 2 prop 3
0.7500000 0.8333333 0.6666667
Warning message:
In prop.test(table) : Chi-squared approximation may be incorrect
I don't understand where I can deduct that Condition1 is more preferred than
Conditions 2 and 3.
Should I simply look at the p-value?
The fact is that tried with a more extreme example, but the p-value results
still above 0.05:
This is the table I used:
> table2
Condition1 Condition2
stimulusA 12 0
stimulusB 10 2
stimulusC 11 1
> table2<-matrix(c(12,0,10,2,11,1),ncol=2,byrow=T)
> rownames(table2)<-c("stimulusA","stimulusB","stimulusC")
> colnames(table2)<-c("Condition1","Condition2")
> prop.test(table2)
3-sample test for equality of proportions without continuity correction
data: table2
X-squared = 2.1818, df = 2, p-value = 0.3359
alternative hypothesis: two.sided
sample estimates:
prop 1 prop 2 prop 3
1.0000000 0.8333333 0.9166667
Warning message:
In prop.test(table2) : Chi-squared approximation may be incorrect
Could you please enlighten me?
Thanks in advance
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