Hi Stan, This is sent to both you and edstat.
"Have you proven that one gas gives better mileage than the other? If so, which one is better?" There are two points. The first is that you have not 'proved' anything - except in the most casual interpretation of 'proof'. What you have done is provide an answer in which you can be very confident to the question posed. So the first amendmentment is to something like: "Can you reasonably conclude that one gas gives better mileage than the other? If so, which one is better?" Second, the question is confusingly - sloppily - posed. It appears to be two questions. The first leads to a two tailed test - does one gas give better mileage than the other? This is the question that is answered. The second question leads to a one tailed test, which is the one you are trying to answer, I gather as an extra to the original question. As soon as you try to answer both questions simultaneously you run into logical problems. You *have* to be very clear from the start which of the two you are interested in. In this case, do you only want to know (in the sense of 'conclude with some confidence') if: * one gas is better than the other (so you will do a two sided test); or * gas B is better than gas A ( so you will do a two sided test). (You can also pose the question whether gas A is better than gas A, but the sample evidence is obviously against this.) This is one of the bits that causes students most problems - identifying the question being asked! It also seems to be a problem with many researchers, Yet it is fundamental to research..... Happy New Year, Alan Stan Brown wrote: > > I think I've got some sort of mental block on the following point. > Can someone explain this to me, plainly and simply, please? > > Let me start with a sample problem, NOT created by me: > > [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. > > The student is led to a two-sample F test for homoscedasticity; > p=0.1886 so the samples are treated as homoscedastic. Now the > problem says: ] > > "Now the main t-test ... Two Sample Assuming Equal Variances. ... > Use two-tail results (since '=/=' in Ha). ... What is the P-val for > the t-test?" [Answer: p=.0002885] > > "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. > 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. > > 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.) > > -- > Stan Brown, Oak Road Systems, Cortland County, New York, USA > http://oakroadsystems.com/ > "My theory was a perfectly good one. The facts were misleading." > -- /The Lady Vanishes/ (1938) > > ================================================================= > Instructions for joining and leaving this list and remarks about > the problem of INAPPROPRIATE MESSAGES are available at > http://jse.stat.ncsu.edu/ > ================================================================= -- Alan McLean ([EMAIL PROTECTED]) Department of Econometrics and Business Statistics Monash University, Caulfield Campus, Melbourne Tel: +61 03 9903 2102 Fax: +61 03 9903 2007 ================================================================= Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =================================================================
