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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
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I do not know where else to put it, so I'll ask this here. Dear user4701 - I am just curious, were none of the answers to the 5 other questions that you have asked so far on CV adequate enough to warrant accepting at least one of the answers as the correct/best one? I also do not see many upvotes for the extensive comments that you have received. Please remember that people are taking time out of their busy schedules to answer your questions. That is your way of rewarding that effort! – Wolfgang Aug 22 '11 at 10:54
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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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1 Answer

up vote 3 down vote accepted

Under the null hypothesis (that Techniques 1 and 2 are each equally preferred), you can combine across experiments, and so just compare the overall results (23 for technique 1 and 7 for technique 2). I would use then use an exact binomial test.

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).

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Dear Karl, thanks a lot. I found your comment very useful. Many thanks – Luca Sep 3 '11 at 19:38

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