Rich Ulrich <[EMAIL PROTECTED]> wrote in sci.stat.edu:
>[ posted and e-mailed.]
Ditto.
>On Sat, 29 Dec 2001 16:46:10 -0500, [EMAIL PROTECTED] (Stan Brown)
>wrote:
>> 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.
Hmm... Which "earlier statement" do you mean? If two means are
different then one of them _must_ be larger than the other; that's
how real numbers work. Can you explain your raised eyebrow a bit
more specifically? Or is it just the word "proven", about which I
comment below.
> 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?]
No; this was in a book of homework problems, which is pretty
standard at the junior college where I teach. Specifically, it was a
lengthy exercise in using Excel to do the sort of statistical tests
the students normally do on a TI83.
>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?
All good points for discussion. But I wouldn't focus too much on
that off-the-cuff word "prove". (I'm not being defensive since I
didn't write the exercise. :-) My students did understand that
nothing is ever proved; that there's still a p-value chance of
getting the sample results you got even if you did perfect random
selection an d the null hypothesis is true. Maybe I'm being UNDER-
scrupulous here, but I think it a pardonable bit of sloppy language.
>> 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?
I added that for purposes of posting; the original exercise didn't
have the students do a one-tailed test at all. It's just half the
two-tailed p-value, as I'm sure you recognize.
>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.
Well, these two p-values are smaller than that: you're talking
significance level of 0.1% and these were 0.014% or 0.029%.
But my question was not about reporting a smaller p-value; it was
about first establishing a two-tailed "difference" and then moving
from that to declaring which side the difference lies on. I think
A.G. McDowell has disposed of that, however.
--
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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