Sides? Tails?
There are hypotheses that are one- or two-sided.
There are distributions (like the t) that are sometimes
folded over, in order report "two tails" worth of p-level
for the amount of the extreme.
I don't like to write about these, because it is so easy
to be careless and write it wrong -- there is not an official
terminology.
On Thu, 15 Mar 2001 14:29:04 GMT, Jerry Dallal
<[EMAIL PROTECTED]> wrote:
> We don't really disagree. Any apparent disagreement is probably due
> to the abbreviated kind of discussion that takes place in Usenet.
> See http://www.tufts.edu/~gdallal/onesided.htm
>
> Alan McLean ([EMAIL PROTECTED]) wrote:
>
> > My point however is still true - that the person who receives
> > the control treatment is presumably getting an inferior treatment. You
> > certainly don't test a new treatment if you think it is worse than
> > nothing, or worse than current treatments!
>
> Equipoise demands the investigator be uncertain of the direction.
> The problem with one-tailed tests is that they imply the irrelevance
> of differences in a particular direction. I've yet to meet the
> researcher who is willing to say they are irrelevant regardless of
> what they might be.
[ ... ]
"Equipoise"? I'm not familiar with that as a principle, though I
would guess....
When I was taught testing, I was taught that using *one* tail
of a distribution is what is statistically intelligible, or natural.
Adding together the opposite extremes of the CDF, as with a
"two-tailed t-test," is an arbitrary act. It seems to be justified
or explained by pointing to the relation between tests on
two means, t^2 = F. Is that explanation enough?
Technically speaking (as I was taught, and as it still
seems to me), there is nothing wrong with electing to
take 4.5% from one tail, and 0.5% from the other tail.
Someone has complained about this: that is "really"
what some experimenters do. They say they plan a
one-tailed t- test of a one-sided hypothesis. However,
they do not *dismiss* a big effect in the wrong direction,
but they want to apply different values to it. I say, This
does make sense, if you set up the tests like I just said.
That is: I ask, What is believable?
Yes, to a 4.4% test (for instance) in the expected direction.
No, to a test of 2% or 1% or so, in the other direction;
- but: Pay attention, if it is EXTREME enough.
Notice, you can take out a 0.1% test and leave the main
test as 4.9%, which is not effectively different from 5%.
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
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