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I gathered 11 responses to a question where the options were A, B, or C.

9 people answered A. 2 people answered B. 0 people answered C.

Using Clopper-Pearson 95% confidence intervals, I obtained that P(A) ranges from (0.48, 0.97), P(B) ranges from (0.2 to 0.52), and P(C) ranges from (0, 0.28).

What statements can I make these results? Can I say that P(A) > P(C) at 95% confidence level? Seems like it would be more than that.

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You are making 3 comparisons instead of one (multiple testing), so you have to account for it in computing you confidence intervals.

Instead of 5% as an acceptable risk, you have to take a lower value like 5%/3=1,66% (Bonferonni correction). In that case you would calculate the 98.34% confidence interval. That way, the global risk to make a wrong conclusion rejecting HO (no difference) across the 3 comparison is truly 5%.

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  • $\begingroup$ Check your calculations. $\endgroup$ – Glen_b Jun 24 '14 at 1:47
  • $\begingroup$ You are right, there was a mistake. Edited. $\endgroup$ – Aurelie Jun 24 '14 at 16:19

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