Question 3: In what way are the confidence intervals contradictory?
The confidence interval for the risk difference contains the null hypothesis value, which is zero. The confidence interval for the risk ratio does not contain the null hypothesis value, which is one. The confidence interval for the odds ratio contains the null hypothesis value, which is one.
Hence one of our confidence intervals, for the risk ratio, suggests that the difference is significant, the others do not. The Fisher's exact test is not significant. This is not a large sample approximation, so it does not have the approximate properties of the confidence intervals and is reliable. The confidence intervals are too narrow.
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Last updated: 20 November, 2006.