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)
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