# How should I use prop.test function?

I did an experiment with 12 participants. They were asked to rate 3 stimuli, with the following 3 possible answers: "increased", "decreased", "no difference". I have as a result this table:

          Increase Decreased No_difference

StimulusA   10      1           1
StimulusB   12      0           0
StimulusC    8      2           2


Now,if I want to understand in one shot if the "Increase" answer is chosen significantly more than the other two answers in all the Stimuli, is it correct if I simply use the binomial distribution summing the successes along all the 3 stimuli?

I mean, is it correct doing this?

> prop.test(30,36)

1-sample proportions test with continuity correction

data:  30 out of 36, null probability 0.5
X-squared = 14.6944, df = 1, p-value = 0.0001264
alternative hypothesis: true p is not equal to 0.5
95 percent confidence interval:
0.6652978 0.9303666
sample estimates:
p
0.8333333


Or it is better to use the function in this way instead?

> prop.test(c(10,12,8),c(12,12,12),c(0.5,0.5,0.5))

3-sample test for given proportions without continuity correction

data:  c(10, 12, 8) out of c(12, 12, 12), null probabilities c(0.5, 0.5, 0.5)
X-squared = 18.6667, df = 3, p-value = 0.0003204
alternative hypothesis: two.sided
null values:
prop 1 prop 2 prop 3
0.5    0.5    0.5
sample estimates:
prop 1    prop 2    prop 3
0.8333333 1.0000000 0.6666667


prop.test(30,36, p=0.5, "greater")