StATS: Perfect isn't quite good enough (December 12, 2006)

Someone wanted me to double check their calculations for Fisher's Exact test. If the control group, 3 out of 10 patients experienced an unfortunate outcome. In the treatment group none did (out of 6). You would think that a perfect result in the treatment group would be compelling, but the one-sided p-value for Fisher's Exact test is 0.21.

That calculation is a bit disappointing, but perhaps not too surprising. The rule of three states that when you observe zero events in a sample of n patients, then 3/n is an approximate upper 95% confidence interval. So with 0/6, that upper limit would be 3/6 or 50% which is well above the control rate of 30%.  So perfection just isn't good enough when you have such small sample sizes.

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This page was written by Steve Simon while working at Children's Mercy Hospital. Although I do not hold the copyright for this material, I am reproducing it here as a service, as it is no longer available on the Children's Mercy Hospital website. Need more information? I have a page with general help resources. You can also browse for pages similar to this one at Category: Small sample size issues.