[Stan: Please observe that this is copied to edstat. -- Don.]
On Sat, 29 Dec 2001, 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:
< snip, details of two-sample t test, two-sided >
> "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 (>)?
In the nature of a two-tailed test, if it is rejected, the data must have
resided in one of the two tails; can't reject if it's in the middle.
What objection can there be to reporting which tail the data actually
landed in?
That the _test_ is two-sided merely means that one is not imposing a
prior prejudice (I know, it's redundant; useful emphasis) on the outcome
of the _test_: one will reject if the outcome is > than the value
specified in the null hypothesis, OR if the outcome is < than that value.
Having rejected the null, one surely knows in which direction it was
rejected (that is, in which tail the test statistic appeared), and it is
surely proper to report that piece of information. (In fact, I would
consider it improper, as well as incomplete, NOT to report it.)
> 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.
Then I take it you would also consider it "smarmy" to report the result
of a post hoc contrast (let alone a series of such contrasts) following
a significant F-test in an ANOVA? Same principle: a two-sample t-test
is the same thing as an ANOVA on two groups, and following a significant
F with the one possible contrast that can be defined, the value of the
contrast is either negative or positive, and that sign dtermines which
group has the higher mean.
> Am I being over-scrupulous here?
Dunno about "over-scrupulous". Illogical, though.
-- DFB.
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Donald F. Burrill [EMAIL PROTECTED]
184 Nashua Road, Bedford, NH 03110 603-471-7128
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