StATS: Statistical koan #2 (Feburary 28, 2006)

I got some limited feedback from EDSTAT-L about using koans to illustrate difficult and subtle statistical concepts, and at least one person thought that this device would end up confusing people more than helping them. With that in mind, here is a second koan. Let me know if it confuses more than it helps.

Master Stem was inspecting his students work. Student Leaf displayed a 95% confidence interval from a randomized control trial. "What does this confidence interval tell you?" Master Stem inquired.

Student Leaf replied, "This interval contains the value of zero, which provides evidence that there is no difference between the treatment group and the control group."

"And what can you tell me about the truth of this interval, Student Leaf."

"We cannot make a probability statement about this particular interval, Master Stem. We can say, however, that if I collected 100 samples and computed confidence intervals using this method, about 95% of them would contain the true mean difference."

"Very interesting, Student Leaf. Now that you have collected the first sample, when do you plan on collecting the other 99?"

I should probably attach titles to these koans. The first koan could be

and the second one could be

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