# one-tailed or two-tailed. which is right?

Discussion in 'SPSS' started by Mike, Oct 29, 2011.

1. ### MikeGuest

Hi,
Say, alpha=0.05 and I get p=0.08 when I compare two indepdent-sample
means.
If H1 mu1<>mu2, then I should not reject H0. This is two-tailed test.
For one-tailed test, p is 0.08/2. right?
If H1 mu1> or < mu2, then I should reject H0. This is one-tailed test.
The result is mu1=mu2, but mu1> or < mu2.
How to explain this? I am very confused.
Mike

Mike, Oct 29, 2011

2. ### Rich UlrichGuest

The null hypothesis must be chosen before the data are
examined at all. If you are replicating something that is well
known, you *might* be able to justify a one-tailed test.
Or, some reviewers or editors who are suspicious of "convenient
choices" might object to your one-tailed test, anyway.

If the null hypothesis says that mu1 < mu2, then no matter
*how* big the difference is for mu1 >> mu2 -- if that is how
the result came out -- you would be forced to conclude
"No Difference". Observing a huge effect in the wrong
direction is only "suggestive" at best, just like seeing an
effect with p-value of 0.12 or whatever is non-significant.

But it doesn't have to be that way.

The formal convention is to assign half of the "rejection region"
to each side of the test. Technically, that is a convention,
not a law. In practice, we sometimes tend to act as if we
were observing a different convention, to the effect that we
take something like "0.001" in the "wrong" direction, and the
rest of the 0.05 is the "right" direction. Thus, we might be
willing to act pretty much like an effect is "real" when it hits
0.001 in the wrong direction, even though that was the
wrong direction.

Rich Ulrich, Oct 29, 2011

3. ### Bruce WeaverGuest

I think Rich meant *alternative* hypothesis on that line. In the most
common application of hypothesis testing, it is the alternative
hypothesis that is either directional or non-directional (i.e.,
one-tailed or two-tailed).

While I agree with you, Rich, I think that reviewers and editors might
again become suspicious if one actually tried this.

Bruce Weaver, Oct 30, 2011