[ posted and e-mailed.] On Sat, 29 Dec 2001 16:46:10 -0500, [EMAIL PROTECTED] (Stan Brown) wrote:
[... ] > > [The student is led to enter two sets of unpaired figures into > Excel. They represent miles per gallon with gasoline A and gasoline > B. I won't give the actual figures, but here's a summary: > > A: mean = 21.9727, variance = 0.4722, n = 11 > B: mean = 22.9571, variance = 0.2165, n = 14 > > The question is whether there is a difference in gasoline mileage. [snip, about variances.] > > "What's your conclusion about the difference in gas mileage?" > [Answer: At significance level 5%, previously selected, there is a > difference between them.] > > Now we come to the part I'm having conceptual trouble with: "Have > you proven that one gas gives better mileage than the other? If so, > which one is better?" > > Now obviously if the two are different then one is better, and if > one is better it's probably B since B had the higher sample mean. I want to raise an eyebrow at this earlier statement. We should not overlook the chance to teach our budding statisticians: *Always* pay attention to the distinction between random trials or careful controls, on the one hand; and grab-samples on the other. [Maybe your teacher asked the question that way, in order to lead up to that in class?] The numbers do not *prove* that one gas gives better mileage; the mileage was, indeed, better for one gas than another -- for reasons yet to be discussed. Different cars? drivers? routes? > But are we in fact justified in jumping from a two-tailed test (=/=) > to a one-tailed result (>)? > > Here we have a tiny p-value, and in fact a one-tailed test gives a > p-value of 0.0001443. But something seems a little smarmy about > first setting out to discover whether there is a difference -- just > a difference, unequal means -- then computing a two-tailed test and > deciding to announce a one-tailed result. Another small issue. Why did the .00014 appear? In clinical trials, we observe the difference and then we do attribute it to one end. But it is not the convention to report the one-tailed p-level, after the fact. I think there are editors who would object to that, but that is a guess. Also, for various reasons, our smallest p-level for reporting is usually 0.001. > > Am I being over-scrupulous here? Am I not even asking the right > question? Thanks for any enlightenment. > > (If you send me an e-mail copy of a public follow-up, please let me > know that it's a copy so I know to reply publicly.) -- Rich Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html ================================================================= Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =================================================================
