# How to test whether percentage is significantly greater than 50% after averaging across three experiments?

### Context:

I ran 3 experiments comparing in each 2 techniques. In each experiment participants had simply to express a preference about which of the 2 techniques they thought was clearest to understand.

30 participants were involved, 10 in each experiment. No repeated measures were involved.

Now I have a table of the results like so:

            Technique 1   Technique 2
EXP1:   80%           20%
EXP2:   90%           10%
EXP3:   60%           40%


I want to know if globally technique 1 is statistically significantly better than technique 2.

### Questions:

• Which analysis should I perform?
• How could this be done in R?
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How do the three experiments differ? or are they just replications? –  Jeromy Anglim Aug 22 '11 at 7:36
Following up on Wolfgang's comment, if a question you have asked has received a good answer, then as described here, you should click the check next to the answer that you find most helpful. –  Karl Aug 22 '11 at 11:47
Dear all, sorry for my delay. I did a car accident and I was at the hospital for 9 days. It is not true that I don´t thank, I always thank everybody for their effort. Always. I read your e-mail only now. I am sorry to reply now, but I have had such big problems. –  Luca Sep 3 '11 at 19:35
Dear Jeromy, the three experiments were different but tested the same thing, just in three different conditions. –  Luca Sep 3 '11 at 19:39
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In R: binom.test(23, 30), which gives a p-value of 0.005. It also gives a confidence interval for the preference for technique 1, (0.58, 0.90).